x(2x+9)=518

Solution for x(2x+9)=518 equation:

x(2x+9)=518

We move all terms to the left:

x(2x+9)-(518)=0

We multiply parentheses

2x^2+9x-518=0

a = 2; b = 9; c = -518;
Δ = b2-4ac
Δ = 92-4·2·(-518)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-65}{2*2}=\frac{-74}{4}
=-18+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+65}{2*2}=\frac{56}{4}
=14
$