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x^{2}=\frac{9}{8}
Divide both sides by 8.
x=\frac{3\sqrt{2}}{4} x=-\frac{3\sqrt{2}}{4}
Take the square root of both sides of the equation.
x^{2}=\frac{9}{8}
Divide both sides by 8.
x^{2}-\frac{9}{8}=0
Subtract \frac{9}{8} from both sides.
x=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{8}\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{9}{8} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-\frac{9}{8}\right)}}{2}
Square 0.
x=\frac{0±\sqrt{\frac{9}{2}}}{2}
Multiply -4 times -\frac{9}{8}.
x=\frac{0±\frac{3\sqrt{2}}{2}}{2}
Take the square root of \frac{9}{2}.
x=\frac{3\sqrt{2}}{4}
Now solve the equation x=\frac{0±\frac{3\sqrt{2}}{2}}{2} when ± is plus.
x=-\frac{3\sqrt{2}}{4}
Now solve the equation x=\frac{0±\frac{3\sqrt{2}}{2}}{2} when ± is minus.
x=\frac{3\sqrt{2}}{4} x=-\frac{3\sqrt{2}}{4}
The equation is now solved.