Solve for x
x=\frac{\sqrt{6}}{3}\approx 0.816496581
x=-\frac{\sqrt{6}}{3}\approx -0.816496581
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3x^{2}=8-6
Subtract 6 from both sides.
3x^{2}=2
Subtract 6 from 8 to get 2.
x^{2}=\frac{2}{3}
Divide both sides by 3.
x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}
Take the square root of both sides of the equation.
3x^{2}+6-8=0
Subtract 8 from both sides.
3x^{2}-2=0
Subtract 8 from 6 to get -2.
x=\frac{0±\sqrt{0^{2}-4\times 3\left(-2\right)}}{2\times 3}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 3\left(-2\right)}}{2\times 3}
Square 0.
x=\frac{0±\sqrt{-12\left(-2\right)}}{2\times 3}
Multiply -4 times 3.
x=\frac{0±\sqrt{24}}{2\times 3}
Multiply -12 times -2.
x=\frac{0±2\sqrt{6}}{2\times 3}
Take the square root of 24.
x=\frac{0±2\sqrt{6}}{6}
Multiply 2 times 3.
x=\frac{\sqrt{6}}{3}
Now solve the equation x=\frac{0±2\sqrt{6}}{6} when ± is plus.
x=-\frac{\sqrt{6}}{3}
Now solve the equation x=\frac{0±2\sqrt{6}}{6} when ± is minus.
x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}
The equation is now solved.
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