X(-10+4x)=180

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

X(-10+4X)=180

We move all terms to the left:

X(-10+4X)-(180)=0

We add all the numbers together, and all the variables

X(4X-10)-180=0

We multiply parentheses

4X^2-10X-180=0

a = 4; b = -10; c = -180;
Δ = b2-4ac
Δ = -102-4·4·(-180)
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{-(-10)-2\sqrt{745}}{2*4}=\frac{10-2\sqrt{745}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{745}}{2*4}=\frac{10+2\sqrt{745}}{8}
$