(18x-9)(4x+13)=90

Solution for (18x-9)(4x+13)=90 equation:

(18x-9)(4x+13)=90

We move all terms to the left:

(18x-9)(4x+13)-(90)=0

We multiply parentheses ..

(+72x^2+234x-36x-117)-90=0

We get rid of parentheses

72x^2+234x-36x-117-90=0

We add all the numbers together, and all the variables

72x^2+198x-207=0

a = 72; b = 198; c = -207;
Δ = b2-4ac
Δ = 1982-4·72·(-207)
Δ = 98820
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:

$\sqrt{\Delta}=\sqrt{98820}=\sqrt{324*305}=\sqrt{324}*\sqrt{305}=18\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(198)-18\sqrt{305}}{2*72}=\frac{-198-18\sqrt{305}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(198)+18\sqrt{305}}{2*72}=\frac{-198+18\sqrt{305}}{144}
$