Solve 600x^2+180x^2-60000=64200

$$600 { x }^{ 2 } +180 { x }^{ 2 } -60000=64200$$

Solve for x

$$x = \frac{3 \sqrt{2990}}{13} \approx 12.61866749$$

$$x = -\frac{3 \sqrt{2990}}{13} \approx -12.61866749$$

Steps by Finding Square Root

Combine 600x^{2} and 180x^{2} to get 780x^{2}.

$$780x^{2}-60000=64200$$

Add 60000 to both sides.

$$780x^{2}=64200+60000$$

Add 64200 and 60000 to get 124200.

$$780x^{2}=124200$$

Divide both sides by 780.

$$x^{2}=\frac{124200}{780}$$

Reduce the fraction \frac{124200}{780} to lowest terms by extracting and canceling out 60.

$$x^{2}=\frac{2070}{13}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{2990}}{13} x=-\frac{3\sqrt{2990}}{13}$$

Steps Using the Quadratic Formula

Combine 600x^{2} and 180x^{2} to get 780x^{2}.

$$780x^{2}-60000=64200$$

Subtract 64200 from both sides.

$$780x^{2}-60000-64200=0$$

Subtract 64200 from -60000 to get -124200.

$$780x^{2}-124200=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 780 for a, 0 for b, and -124200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 780\left(-124200\right)}}{2\times 780}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 780\left(-124200\right)}}{2\times 780}$$

Multiply -4 times 780.

$$x=\frac{0±\sqrt{-3120\left(-124200\right)}}{2\times 780}$$

Multiply -3120 times -124200.

$$x=\frac{0±\sqrt{387504000}}{2\times 780}$$

Take the square root of 387504000.

$$x=\frac{0±360\sqrt{2990}}{2\times 780}$$

Multiply 2 times 780.

$$x=\frac{0±360\sqrt{2990}}{1560}$$

Now solve the equation x=\frac{0±360\sqrt{2990}}{1560} when ± is plus.

$$x=\frac{3\sqrt{2990}}{13}$$

Now solve the equation x=\frac{0±360\sqrt{2990}}{1560} when ± is minus.

$$x=-\frac{3\sqrt{2990}}{13}$$

The equation is now solved.

$$x=\frac{3\sqrt{2990}}{13} x=-\frac{3\sqrt{2990}}{13}$$