(3x+20)(5x-16)=90

Solution for (3x+20)(5x-16)=90 equation:

(3x+20)(5x-16)=90

We move all terms to the left:

(3x+20)(5x-16)-(90)=0

We multiply parentheses ..

(+15x^2-48x+100x-320)-90=0

We get rid of parentheses

15x^2-48x+100x-320-90=0

We add all the numbers together, and all the variables

15x^2+52x-410=0

a = 15; b = 52; c = -410;
Δ = b2-4ac
Δ = 522-4·15·(-410)
Δ = 27304
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:

$\sqrt{\Delta}=\sqrt{27304}=\sqrt{4*6826}=\sqrt{4}*\sqrt{6826}=2\sqrt{6826}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-2\sqrt{6826}}{2*15}=\frac{-52-2\sqrt{6826}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+2\sqrt{6826}}{2*15}=\frac{-52+2\sqrt{6826}}{30}
$