15+(4x-13)(x+18)=180

Solution for 15+(4x-13)(x+18)=180 equation:

15+(4x-13)(x+18)=180

We move all terms to the left:

15+(4x-13)(x+18)-(180)=0

We add all the numbers together, and all the variables

(4x-13)(x+18)-165=0

We multiply parentheses ..

(+4x^2+72x-13x-234)-165=0

We get rid of parentheses

4x^2+72x-13x-234-165=0

We add all the numbers together, and all the variables

4x^2+59x-399=0

a = 4; b = 59; c = -399;
Δ = b2-4ac
Δ = 592-4·4·(-399)
Δ = 9865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-\sqrt{9865}}{2*4}=\frac{-59-\sqrt{9865}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+\sqrt{9865}}{2*4}=\frac{-59+\sqrt{9865}}{8}
$