x^2+9x=234

Solution for x^2+9x=234 equation:

x^2+9x=234

We move all terms to the left:

x^2+9x-(234)=0

a = 1; b = 9; c = -234;
Δ = b2-4ac
Δ = 92-4·1·(-234)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{113}}{2*1}=\frac{-9-3\sqrt{113}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{113}}{2*1}=\frac{-9+3\sqrt{113}}{2}
$