9x^2-30=2x

Solution for 9x^2-30=2x equation:

9x^2-30=2x

We move all terms to the left:

9x^2-30-(2x)=0

a = 9; b = -2; c = -30;
Δ = b2-4ac
Δ = -22-4·9·(-30)
Δ = 1084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1084}=\sqrt{4*271}=\sqrt{4}*\sqrt{271}=2\sqrt{271}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{271}}{2*9}=\frac{2-2\sqrt{271}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{271}}{2*9}=\frac{2+2\sqrt{271}}{18}
$