(3x+18)(9x-27)=90

Solution for (3x+18)(9x-27)=90 equation:

(3x+18)(9x-27)=90

We move all terms to the left:

(3x+18)(9x-27)-(90)=0

We multiply parentheses ..

(+27x^2-81x+162x-486)-90=0

We get rid of parentheses

27x^2-81x+162x-486-90=0

We add all the numbers together, and all the variables

27x^2+81x-576=0

a = 27; b = 81; c = -576;
Δ = b2-4ac
Δ = 812-4·27·(-576)
Δ = 68769
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:

$\sqrt{\Delta}=\sqrt{68769}=\sqrt{81*849}=\sqrt{81}*\sqrt{849}=9\sqrt{849}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-9\sqrt{849}}{2*27}=\frac{-81-9\sqrt{849}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+9\sqrt{849}}{2*27}=\frac{-81+9\sqrt{849}}{54}
$