Solve 2/3x^2+35=87

$$\frac { 2 } { 3 } x ^ { 2 } + 35 = 87$$

Solve for x

$$x=\sqrt{78}\approx 8.831760866$$

$$x=-\sqrt{78}\approx -8.831760866$$

Steps by Finding Square Root

Subtract 35 from both sides.

$$\frac{2}{3}x^{2}=87-35$$

Subtract 35 from 87 to get 52.

$$\frac{2}{3}x^{2}=52$$

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$x^{2}=52\times \frac{3}{2}$$

Multiply 52 and \frac{3}{2} to get 78.

$$x^{2}=78$$

Take the square root of both sides of the equation.

$$x=\sqrt{78} x=-\sqrt{78}$$

Steps Using the Quadratic Formula

Subtract 87 from both sides.

$$\frac{2}{3}x^{2}+35-87=0$$

Subtract 87 from 35 to get -52.

$$\frac{2}{3}x^{2}-52=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{2}{3} for a, 0 for b, and -52 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{2}{3}\left(-52\right)}}{2\times \frac{2}{3}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{2}{3}\left(-52\right)}}{2\times \frac{2}{3}}$$

Multiply -4 times \frac{2}{3}.

$$x=\frac{0±\sqrt{-\frac{8}{3}\left(-52\right)}}{2\times \frac{2}{3}}$$

Multiply -\frac{8}{3} times -52.

$$x=\frac{0±\sqrt{\frac{416}{3}}}{2\times \frac{2}{3}}$$

Take the square root of \frac{416}{3}.

$$x=\frac{0±\frac{4\sqrt{78}}{3}}{2\times \frac{2}{3}}$$

Multiply 2 times \frac{2}{3}.

$$x=\frac{0±\frac{4\sqrt{78}}{3}}{\frac{4}{3}}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{78}}{3}}{\frac{4}{3}} when ± is plus.

$$x=\sqrt{78}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{78}}{3}}{\frac{4}{3}} when ± is minus.

$$x=-\sqrt{78}$$

The equation is now solved.

$$x=\sqrt{78} x=-\sqrt{78}$$