(4x+2)(5x-15)=90

Solution for (4x+2)(5x-15)=90 equation:

(4x+2)(5x-15)=90

We move all terms to the left:

(4x+2)(5x-15)-(90)=0

We multiply parentheses ..

(+20x^2-60x+10x-30)-90=0

We get rid of parentheses

20x^2-60x+10x-30-90=0

We add all the numbers together, and all the variables

20x^2-50x-120=0

a = 20; b = -50; c = -120;
Δ = b2-4ac
Δ = -502-4·20·(-120)
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-110}{2*20}=\frac{-60}{40}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+110}{2*20}=\frac{160}{40}
=4
$