(x-18)(3x+16)=90

Solution for (x-18)(3x+16)=90 equation:

(x-18)(3x+16)=90

We move all terms to the left:

(x-18)(3x+16)-(90)=0

We multiply parentheses ..

(+3x^2+16x-54x-288)-90=0

We get rid of parentheses

3x^2+16x-54x-288-90=0

We add all the numbers together, and all the variables

3x^2-38x-378=0

a = 3; b = -38; c = -378;
Δ = b2-4ac
Δ = -382-4·3·(-378)
Δ = 5980
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:

$\sqrt{\Delta}=\sqrt{5980}=\sqrt{4*1495}=\sqrt{4}*\sqrt{1495}=2\sqrt{1495}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{1495}}{2*3}=\frac{38-2\sqrt{1495}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{1495}}{2*3}=\frac{38+2\sqrt{1495}}{6}
$