Solve for x
x=\sqrt{6}\approx 2.449489743
x=-\sqrt{6}\approx -2.449489743
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4x^{2}=30-6
Subtract 6 from both sides.
4x^{2}=24
Subtract 6 from 30 to get 24.
x^{2}=\frac{24}{4}
Divide both sides by 4.
x^{2}=6
Divide 24 by 4 to get 6.
x=\sqrt{6} x=-\sqrt{6}
Take the square root of both sides of the equation.
4x^{2}+6-30=0
Subtract 30 from both sides.
4x^{2}-24=0
Subtract 30 from 6 to get -24.
x=\frac{0±\sqrt{0^{2}-4\times 4\left(-24\right)}}{2\times 4}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 4\left(-24\right)}}{2\times 4}
Square 0.
x=\frac{0±\sqrt{-16\left(-24\right)}}{2\times 4}
Multiply -4 times 4.
x=\frac{0±\sqrt{384}}{2\times 4}
Multiply -16 times -24.
x=\frac{0±8\sqrt{6}}{2\times 4}
Take the square root of 384.
x=\frac{0±8\sqrt{6}}{8}
Multiply 2 times 4.
x=\sqrt{6}
Now solve the equation x=\frac{0±8\sqrt{6}}{8} when ± is plus.
x=-\sqrt{6}
Now solve the equation x=\frac{0±8\sqrt{6}}{8} when ± is minus.
x=\sqrt{6} x=-\sqrt{6}
The equation is now solved.
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