(x-5)(2x+3)=180

Solution for (x-5)(2x+3)=180 equation:

(x-5)(2x+3)=180

We move all terms to the left:

(x-5)(2x+3)-(180)=0

We multiply parentheses ..

(+2x^2+3x-10x-15)-180=0

We get rid of parentheses

2x^2+3x-10x-15-180=0

We add all the numbers together, and all the variables

2x^2-7x-195=0

a = 2; b = -7; c = -195;
Δ = b2-4ac
Δ = -72-4·2·(-195)
Δ = 1609
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{-(-7)-\sqrt{1609}}{2*2}=\frac{7-\sqrt{1609}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1609}}{2*2}=\frac{7+\sqrt{1609}}{4}
$