(x+3)(2x-3)=90

Solution for (x+3)(2x-3)=90 equation:

(x+3)(2x-3)=90

We move all terms to the left:

(x+3)(2x-3)-(90)=0

We multiply parentheses ..

(+2x^2-3x+6x-9)-90=0

We get rid of parentheses

2x^2-3x+6x-9-90=0

We add all the numbers together, and all the variables

2x^2+3x-99=0

a = 2; b = 3; c = -99;
Δ = b2-4ac
Δ = 32-4·2·(-99)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{89}}{2*2}=\frac{-3-3\sqrt{89}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{89}}{2*2}=\frac{-3+3\sqrt{89}}{4}
$