(x-10)(2x+19)=180

Solution for (x-10)(2x+19)=180 equation:

(x-10)(2x+19)=180

We move all terms to the left:

(x-10)(2x+19)-(180)=0

We multiply parentheses ..

(+2x^2+19x-20x-190)-180=0

We get rid of parentheses

2x^2+19x-20x-190-180=0

We add all the numbers together, and all the variables

2x^2-1x-370=0

a = 2; b = -1; c = -370;
Δ = b2-4ac
Δ = -12-4·2·(-370)
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{-(-1)-3\sqrt{329}}{2*2}=\frac{1-3\sqrt{329}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{329}}{2*2}=\frac{1+3\sqrt{329}}{4}
$