x^2-18x+4x=180

Solution for x^2-18x+4x=180 equation:

x^2-18x+4x=180

We move all terms to the left:

x^2-18x+4x-(180)=0

We add all the numbers together, and all the variables

x^2-14x-180=0

a = 1; b = -14; c = -180;
Δ = b2-4ac
Δ = -142-4·1·(-180)
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{229}}{2*1}=\frac{14-2\sqrt{229}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{229}}{2*1}=\frac{14+2\sqrt{229}}{2}
$