(x-5)(4x-10)=180

Solution for (x-5)(4x-10)=180 equation:

(x-5)(4x-10)=180

We move all terms to the left:

(x-5)(4x-10)-(180)=0

We multiply parentheses ..

(+4x^2-10x-20x+50)-180=0

We get rid of parentheses

4x^2-10x-20x+50-180=0

We add all the numbers together, and all the variables

4x^2-30x-130=0

a = 4; b = -30; c = -130;
Δ = b2-4ac
Δ = -302-4·4·(-130)
Δ = 2980
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:

$\sqrt{\Delta}=\sqrt{2980}=\sqrt{4*745}=\sqrt{4}*\sqrt{745}=2\sqrt{745}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{745}}{2*4}=\frac{30-2\sqrt{745}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{745}}{2*4}=\frac{30+2\sqrt{745}}{8}
$