(5x+1)(8x-20)=180

Solution for (5x+1)(8x-20)=180 equation:

(5x+1)(8x-20)=180

We move all terms to the left:

(5x+1)(8x-20)-(180)=0

We multiply parentheses ..

(+40x^2-100x+8x-20)-180=0

We get rid of parentheses

40x^2-100x+8x-20-180=0

We add all the numbers together, and all the variables

40x^2-92x-200=0

a = 40; b = -92; c = -200;
Δ = b2-4ac
Δ = -922-4·40·(-200)
Δ = 40464
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:

$\sqrt{\Delta}=\sqrt{40464}=\sqrt{144*281}=\sqrt{144}*\sqrt{281}=12\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-12\sqrt{281}}{2*40}=\frac{92-12\sqrt{281}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+12\sqrt{281}}{2*40}=\frac{92+12\sqrt{281}}{80}
$