Solve 6-1/3x^2=-20

$$6 - \frac { 1 } { 3 } x ^ { 2 } = - 20$$

Solve for x

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

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

Steps by Finding Square Root

Subtract 6 from both sides.

$$-\frac{1}{3}x^{2}=-20-6$$

Subtract 6 from -20 to get -26.

$$-\frac{1}{3}x^{2}=-26$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

$$x^{2}=-26\left(-3\right)$$

Multiply -26 and -3 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

Add 20 to both sides.

$$6-\frac{1}{3}x^{2}+20=0$$

Add 6 and 20 to get 26.

$$26-\frac{1}{3}x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-\frac{1}{3}x^{2}+26=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{3} for a, 0 for b, and 26 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{3}\right)\times 26}}{2\left(-\frac{1}{3}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{3}\right)\times 26}}{2\left(-\frac{1}{3}\right)}$$

Multiply -4 times -\frac{1}{3}.

$$x=\frac{0±\sqrt{\frac{4}{3}\times 26}}{2\left(-\frac{1}{3}\right)}$$

Multiply \frac{4}{3} times 26.

$$x=\frac{0±\sqrt{\frac{104}{3}}}{2\left(-\frac{1}{3}\right)}$$

Take the square root of \frac{104}{3}.

$$x=\frac{0±\frac{2\sqrt{78}}{3}}{2\left(-\frac{1}{3}\right)}$$

Multiply 2 times -\frac{1}{3}.

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

Now solve the equation x=\frac{0±\frac{2\sqrt{78}}{3}}{-\frac{2}{3}} when ± is plus.

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

Now solve the equation x=\frac{0±\frac{2\sqrt{78}}{3}}{-\frac{2}{3}} when ± is minus.

$$x=\sqrt{78}$$

The equation is now solved.

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