1. **Stating the problem:** Solve the equation $$\left(112128.28-60\cdot x^2\right)\cdot \left(46135.98-28.03\cdot x^2\right)-\left(-46135.98\right)^2=0.$$\n\n2. **Rewrite the equation:** Let us denote $$a=112128.28,\ b=60,\ c=46135.98,\ d=28.03.$$ The equation becomes $$\left(a - b x^2\right)\left(c - d x^2\right) - (-c)^2 = 0.$$\n\n3. **Expand the product:**\n$$\left(a - b x^2\right)\left(c - d x^2\right) = a c - a d x^2 - b c x^2 + b d x^4.$$\n\n4. **Substitute back and simplify:**\n$$a c - a d x^2 - b c x^2 + b d x^4 - c^2 = 0.$$\n\n5. **Group like terms:**\n$$b d x^4 - (a d + b c) x^2 + (a c - c^2) = 0.$$\n\n6. **Calculate constants:**\n$$a c = 112128.28 \times 46135.98 = 5174049273.6584,$$\n$$a d = 112128.28 \times 28.03 = 3140950.4084,$$\n$$b c = 60 \times 46135.98 = 2768158.8,$$\n$$b d = 60 \times 28.03 = 1681.8,$$\n$$c^2 = (46135.98)^2 = 2128469996.9604.$$\n\n7. **Rewrite the quartic in terms of $y = x^2$:**\n$$1681.8 y^2 - (3140950.4084 + 2768158.8) y + (5174049273.6584 - 2128469996.9604) = 0,$$\nwhich simplifies to\n$$1681.8 y^2 - 5909109.2084 y + 3045579276.698 = 0.$$\n\n8. **Divide entire equation by 1681.8 to simplify:**\n$$\cancel{1681.8} y^2 - \frac{5909109.2084}{\cancel{1681.8}} y + \frac{3045579276.698}{\cancel{1681.8}} = 0,$$\nwhich is\n$$y^2 - 3511.5 y + 1810000 = 0.$$\n\n9. **Solve quadratic equation for $y$ using the quadratic formula:**\n$$y = \frac{3511.5 \pm \sqrt{3511.5^2 - 4 \times 1 \times 1810000}}{2}.$$\nCalculate discriminant:\n$$\Delta = 3511.5^2 - 4 \times 1810000 = 12333122.25 - 7240000 = 5093122.25.$$\n\n10. **Calculate square root of discriminant:**\n$$\sqrt{5093122.25} \approx 2256.8.$$\n\n11. **Find roots for $y$:**\n$$y_1 = \frac{3511.5 + 2256.8}{2} = \frac{5768.3}{2} = 2884.15,$$\n$$y_2 = \frac{3511.5 - 2256.8}{2} = \frac{1254.7}{2} = 627.35.$$\n\n12. **Recall $y = x^2$, so:**\n$$x^2 = 2884.15 \quad \Rightarrow \quad x = \pm \sqrt{2884.15} \approx \pm 53.7,$$\n$$x^2 = 627.35 \quad \Rightarrow \quad x = \pm \sqrt{627.35} \approx \pm 25.05.$$\n\n**Final answer:** $$x \approx \pm 53.7, \pm 25.05.$$