Solve 780x^2-6000=642000

$$780 x ^ { 2 } - 6000 = 642000$$

Solve for x

$$x = \frac{60 \sqrt{39}}{13} \approx 28.823067685$$

$$x = -\frac{60 \sqrt{39}}{13} \approx -28.823067685$$

Steps by Finding Square Root

Add 6000 to both sides.

$$780x^{2}=642000+6000$$

Add 642000 and 6000 to get 648000.

$$780x^{2}=648000$$

Divide both sides by 780.

$$x^{2}=\frac{648000}{780}$$

Reduce the fraction \frac{648000}{780} to lowest terms by extracting and canceling out 60.

$$x^{2}=\frac{10800}{13}$$

Take the square root of both sides of the equation.

$$x=\frac{60\sqrt{39}}{13} x=-\frac{60\sqrt{39}}{13}$$

Steps Using the Quadratic Formula

Subtract 642000 from both sides.

$$780x^{2}-6000-642000=0$$

Subtract 642000 from -6000 to get -648000.

$$780x^{2}-648000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 780 for a, 0 for b, and -648000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 780\left(-648000\right)}}{2\times 780}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 780\left(-648000\right)}}{2\times 780}$$

Multiply -4 times 780.

$$x=\frac{0±\sqrt{-3120\left(-648000\right)}}{2\times 780}$$

Multiply -3120 times -648000.

$$x=\frac{0±\sqrt{2021760000}}{2\times 780}$$

Take the square root of 2021760000.

$$x=\frac{0±7200\sqrt{39}}{2\times 780}$$

Multiply 2 times 780.

$$x=\frac{0±7200\sqrt{39}}{1560}$$

Now solve the equation x=\frac{0±7200\sqrt{39}}{1560} when ± is plus.

$$x=\frac{60\sqrt{39}}{13}$$

Now solve the equation x=\frac{0±7200\sqrt{39}}{1560} when ± is minus.

$$x=-\frac{60\sqrt{39}}{13}$$

The equation is now solved.

$$x=\frac{60\sqrt{39}}{13} x=-\frac{60\sqrt{39}}{13}$$