(x-10)(2x+1)=180

Solution for (x-10)(2x+1)=180 equation:

(x-10)(2x+1)=180

We move all terms to the left:

(x-10)(2x+1)-(180)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-19x-190=0

a = 2; b = -19; c = -190;
Δ = b2-4ac
Δ = -192-4·2·(-190)
Δ = 1881
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:

$\sqrt{\Delta}=\sqrt{1881}=\sqrt{9*209}=\sqrt{9}*\sqrt{209}=3\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-3\sqrt{209}}{2*2}=\frac{19-3\sqrt{209}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+3\sqrt{209}}{2*2}=\frac{19+3\sqrt{209}}{4}
$