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3x^{2}=5
Multiply x and x to get x^{2}.
x^{2}=\frac{5}{3}
Divide both sides by 3.
x=\frac{\sqrt{15}}{3} x=-\frac{\sqrt{15}}{3}
Take the square root of both sides of the equation.
3x^{2}=5
Multiply x and x to get x^{2}.
3x^{2}-5=0
Subtract 5 from both sides.
x=\frac{0±\sqrt{0^{2}-4\times 3\left(-5\right)}}{2\times 3}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 3\left(-5\right)}}{2\times 3}
Square 0.
x=\frac{0±\sqrt{-12\left(-5\right)}}{2\times 3}
Multiply -4 times 3.
x=\frac{0±\sqrt{60}}{2\times 3}
Multiply -12 times -5.
x=\frac{0±2\sqrt{15}}{2\times 3}
Take the square root of 60.
x=\frac{0±2\sqrt{15}}{6}
Multiply 2 times 3.
x=\frac{\sqrt{15}}{3}
Now solve the equation x=\frac{0±2\sqrt{15}}{6} when ± is plus.
x=-\frac{\sqrt{15}}{3}
Now solve the equation x=\frac{0±2\sqrt{15}}{6} when ± is minus.
x=\frac{\sqrt{15}}{3} x=-\frac{\sqrt{15}}{3}
The equation is now solved.