X+2x(x-20)=180

Solution for X+2x(x-20)=180 equation:

X+2X(X-20)=180

We move all terms to the left:

X+2X(X-20)-(180)=0

We multiply parentheses

2X^2+X-40X-180=0

We add all the numbers together, and all the variables

2X^2-39X-180=0

a = 2; b = -39; c = -180;
Δ = b2-4ac
Δ = -392-4·2·(-180)
Δ = 2961
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:

$\sqrt{\Delta}=\sqrt{2961}=\sqrt{9*329}=\sqrt{9}*\sqrt{329}=3\sqrt{329}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-3\sqrt{329}}{2*2}=\frac{39-3\sqrt{329}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+3\sqrt{329}}{2*2}=\frac{39+3\sqrt{329}}{4}
$