(5x-4)(2x+20)=180

Solution for (5x-4)(2x+20)=180 equation:

(5x-4)(2x+20)=180

We move all terms to the left:

(5x-4)(2x+20)-(180)=0

We multiply parentheses ..

(+10x^2+100x-8x-80)-180=0

We get rid of parentheses

10x^2+100x-8x-80-180=0

We add all the numbers together, and all the variables

10x^2+92x-260=0

a = 10; b = 92; c = -260;
Δ = b2-4ac
Δ = 922-4·10·(-260)
Δ = 18864
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:

$\sqrt{\Delta}=\sqrt{18864}=\sqrt{144*131}=\sqrt{144}*\sqrt{131}=12\sqrt{131}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-12\sqrt{131}}{2*10}=\frac{-92-12\sqrt{131}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+12\sqrt{131}}{2*10}=\frac{-92+12\sqrt{131}}{20}
$