220=(5x-8)(3x+4)

Solution for 220=(5x-8)(3x+4) equation:

220=(5x-8)(3x+4)

We move all terms to the left:

220-((5x-8)(3x+4))=0

We multiply parentheses ..

-((+15x^2+20x-24x-32))+220=0


We calculate terms in parentheses: -((+15x^2+20x-24x-32)), so:

(+15x^2+20x-24x-32)

We get rid of parentheses

15x^2+20x-24x-32

We add all the numbers together, and all the variables

15x^2-4x-32

Back to the equation:

-(15x^2-4x-32)


We get rid of parentheses

-15x^2+4x+32+220=0

We add all the numbers together, and all the variables

-15x^2+4x+252=0

a = -15; b = 4; c = +252;
Δ = b2-4ac
Δ = 42-4·(-15)·252
Δ = 15136
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:

$\sqrt{\Delta}=\sqrt{15136}=\sqrt{16*946}=\sqrt{16}*\sqrt{946}=4\sqrt{946}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{946}}{2*-15}=\frac{-4-4\sqrt{946}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{946}}{2*-15}=\frac{-4+4\sqrt{946}}{-30}
$