(4x+1)(5x-15)=180

Solution for (4x+1)(5x-15)=180 equation:

(4x+1)(5x-15)=180

We move all terms to the left:

(4x+1)(5x-15)-(180)=0

We multiply parentheses ..

(+20x^2-60x+5x-15)-180=0

We get rid of parentheses

20x^2-60x+5x-15-180=0

We add all the numbers together, and all the variables

20x^2-55x-195=0

a = 20; b = -55; c = -195;
Δ = b2-4ac
Δ = -552-4·20·(-195)
Δ = 18625
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:

$\sqrt{\Delta}=\sqrt{18625}=\sqrt{25*745}=\sqrt{25}*\sqrt{745}=5\sqrt{745}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5\sqrt{745}}{2*20}=\frac{55-5\sqrt{745}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5\sqrt{745}}{2*20}=\frac{55+5\sqrt{745}}{40}
$