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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+4x^2-10x-40x+100)-180=0

We get rid of parentheses

4x^2-10x-40x+100-180=0

We add all the numbers together, and all the variables

4x^2-50x-80=0

a = 4; b = -50; c = -80;
Δ = b2-4ac
Δ = -502-4·4·(-80)
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-6\sqrt{105}}{2*4}=\frac{50-6\sqrt{105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+6\sqrt{105}}{2*4}=\frac{50+6\sqrt{105}}{8}
$