9x^2+3x=52

Solution for 9x^2+3x=52 equation:

9x^2+3x=52

We move all terms to the left:

9x^2+3x-(52)=0

a = 9; b = 3; c = -52;
Δ = b2-4ac
Δ = 32-4·9·(-52)
Δ = 1881
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:

$\sqrt{\Delta}=\sqrt{1881}=\sqrt{9*209}=\sqrt{9}*\sqrt{209}=3\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{209}}{2*9}=\frac{-3-3\sqrt{209}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{209}}{2*9}=\frac{-3+3\sqrt{209}}{18}
$