Solve 6x^2+78=194

$$6 x ^ { 2 } + 78 = 194$$

Solve for x

$$x = \frac{\sqrt{174}}{3} \approx 4.396968653$$

$$x = -\frac{\sqrt{174}}{3} \approx -4.396968653$$

Steps by Finding Square Root

Subtract 78 from both sides.

$$6x^{2}=194-78$$

Subtract 78 from 194 to get 116.

$$6x^{2}=116$$

Divide both sides by 6.

$$x^{2}=\frac{116}{6}$$

Reduce the fraction \frac{116}{6} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{58}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{174}}{3} x=-\frac{\sqrt{174}}{3}$$

Steps Using the Quadratic Formula

Subtract 194 from both sides.

$$6x^{2}+78-194=0$$

Subtract 194 from 78 to get -116.

$$6x^{2}-116=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -116 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-116\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-116\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-116\right)}}{2\times 6}$$

Multiply -24 times -116.

$$x=\frac{0±\sqrt{2784}}{2\times 6}$$

Take the square root of 2784.

$$x=\frac{0±4\sqrt{174}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±4\sqrt{174}}{12}$$

Now solve the equation x=\frac{0±4\sqrt{174}}{12} when ± is plus.

$$x=\frac{\sqrt{174}}{3}$$

Now solve the equation x=\frac{0±4\sqrt{174}}{12} when ± is minus.

$$x=-\frac{\sqrt{174}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{174}}{3} x=-\frac{\sqrt{174}}{3}$$