(x+20)(4x-5)=180

Solution for (x+20)(4x-5)=180 equation:

(x+20)(4x-5)=180

We move all terms to the left:

(x+20)(4x-5)-(180)=0

We multiply parentheses ..

(+4x^2-5x+80x-100)-180=0

We get rid of parentheses

4x^2-5x+80x-100-180=0

We add all the numbers together, and all the variables

4x^2+75x-280=0

a = 4; b = 75; c = -280;
Δ = b2-4ac
Δ = 752-4·4·(-280)
Δ = 10105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-\sqrt{10105}}{2*4}=\frac{-75-\sqrt{10105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+\sqrt{10105}}{2*4}=\frac{-75+\sqrt{10105}}{8}
$