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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+2x^2-3x+6x-9)-180=0

We get rid of parentheses

2x^2-3x+6x-9-180=0

We add all the numbers together, and all the variables

2x^2+3x-189=0

a = 2; b = 3; c = -189;
Δ = b2-4ac
Δ = 32-4·2·(-189)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-39}{2*2}=\frac{-42}{4}
=-10+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+39}{2*2}=\frac{36}{4}
=9
$