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2x^{2}=7-6
Subtract 6 from both sides.
2x^{2}=1
Subtract 6 from 7 to get 1.
x^{2}=\frac{1}{2}
Divide both sides by 2.
x=\frac{\sqrt{2}}{2} x=-\frac{\sqrt{2}}{2}
Take the square root of both sides of the equation.
2x^{2}+6-7=0
Subtract 7 from both sides.
2x^{2}-1=0
Subtract 7 from 6 to get -1.
x=\frac{0±\sqrt{0^{2}-4\times 2\left(-1\right)}}{2\times 2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 2\left(-1\right)}}{2\times 2}
Square 0.
x=\frac{0±\sqrt{-8\left(-1\right)}}{2\times 2}
Multiply -4 times 2.
x=\frac{0±\sqrt{8}}{2\times 2}
Multiply -8 times -1.
x=\frac{0±2\sqrt{2}}{2\times 2}
Take the square root of 8.
x=\frac{0±2\sqrt{2}}{4}
Multiply 2 times 2.
x=\frac{\sqrt{2}}{2}
Now solve the equation x=\frac{0±2\sqrt{2}}{4} when ± is plus.
x=-\frac{\sqrt{2}}{2}
Now solve the equation x=\frac{0±2\sqrt{2}}{4} when ± is minus.
x=\frac{\sqrt{2}}{2} x=-\frac{\sqrt{2}}{2}
The equation is now solved.