Solve {l}{6x+7x+}{8x^2=3}

$$\left. \begin{array} { l } { 6 x + 7 x + } \\ { 8 x ^ { 2 } = 3 } \end{array} \right.$$

Solve for x

$$x=\frac{\sqrt{6}}{4}\approx 0.612372436$$

$$x=-\frac{\sqrt{6}}{4}\approx -0.612372436$$

Steps by Finding Square Root

Divide both sides by 8.

$$x^{2}=\frac{3}{8}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{6}}{4} x=-\frac{\sqrt{6}}{4}$$

Steps Using the Quadratic Formula

Divide both sides by 8.

$$x^{2}=\frac{3}{8}$$

Subtract \frac{3}{8} from both sides.

$$x^{2}-\frac{3}{8}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{3}{8} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{3}{8}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{3}{8}\right)}}{2}$$

Multiply -4 times -\frac{3}{8}.

$$x=\frac{0±\sqrt{\frac{3}{2}}}{2}$$

Take the square root of \frac{3}{2}.

$$x=\frac{0±\frac{\sqrt{6}}{2}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{6}}{2}}{2} when ± is plus.

$$x=\frac{\sqrt{6}}{4}$$

Now solve the equation x=\frac{0±\frac{\sqrt{6}}{2}}{2} when ± is minus.

$$x=-\frac{\sqrt{6}}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{6}}{4} x=-\frac{\sqrt{6}}{4}$$