(x+19)(2x-15)=180

Solution for (x+19)(2x-15)=180 equation:

(x+19)(2x-15)=180

We move all terms to the left:

(x+19)(2x-15)-(180)=0

We multiply parentheses ..

(+2x^2-15x+38x-285)-180=0

We get rid of parentheses

2x^2-15x+38x-285-180=0

We add all the numbers together, and all the variables

2x^2+23x-465=0

a = 2; b = 23; c = -465;
Δ = b2-4ac
Δ = 232-4·2·(-465)
Δ = 4249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{4249}}{2*2}=\frac{-23-\sqrt{4249}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{4249}}{2*2}=\frac{-23+\sqrt{4249}}{4}
$