Solve 30(6x^2-5000)+600x^2=642000

$$30 ( 6 x ^ { 2 } - 5000 ) + 600 x ^ { 2 } = 642000$$

Solve for x

$$x = \frac{20 \sqrt{429}}{13} \approx 31.865100273$$

$$x = -\frac{20 \sqrt{429}}{13} \approx -31.865100273$$

Steps by Finding Square Root

Use the distributive property to multiply 30 by 6x^{2}-5000.

$$180x^{2}-150000+600x^{2}=642000$$

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

$$780x^{2}-150000=642000$$

Add 150000 to both sides.

$$780x^{2}=642000+150000$$

Add 642000 and 150000 to get 792000.

$$780x^{2}=792000$$

Divide both sides by 780.

$$x^{2}=\frac{792000}{780}$$

Reduce the fraction \frac{792000}{780} to lowest terms by extracting and canceling out 60.

$$x^{2}=\frac{13200}{13}$$

Take the square root of both sides of the equation.

$$x=\frac{20\sqrt{429}}{13} x=-\frac{20\sqrt{429}}{13}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 30 by 6x^{2}-5000.

$$180x^{2}-150000+600x^{2}=642000$$

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

$$780x^{2}-150000=642000$$

Subtract 642000 from both sides.

$$780x^{2}-150000-642000=0$$

Subtract 642000 from -150000 to get -792000.

$$780x^{2}-792000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 780 for a, 0 for b, and -792000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 780\left(-792000\right)}}{2\times 780}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 780\left(-792000\right)}}{2\times 780}$$

Multiply -4 times 780.

$$x=\frac{0±\sqrt{-3120\left(-792000\right)}}{2\times 780}$$

Multiply -3120 times -792000.

$$x=\frac{0±\sqrt{2471040000}}{2\times 780}$$

Take the square root of 2471040000.

$$x=\frac{0±2400\sqrt{429}}{2\times 780}$$

Multiply 2 times 780.

$$x=\frac{0±2400\sqrt{429}}{1560}$$

Now solve the equation x=\frac{0±2400\sqrt{429}}{1560} when ± is plus.

$$x=\frac{20\sqrt{429}}{13}$$

Now solve the equation x=\frac{0±2400\sqrt{429}}{1560} when ± is minus.

$$x=-\frac{20\sqrt{429}}{13}$$

The equation is now solved.

$$x=\frac{20\sqrt{429}}{13} x=-\frac{20\sqrt{429}}{13}$$