(2x-1)(3x+5)=180

Solution for (2x-1)(3x+5)=180 equation:

(2x-1)(3x+5)=180

We move all terms to the left:

(2x-1)(3x+5)-(180)=0

We multiply parentheses ..

(+6x^2+10x-3x-5)-180=0

We get rid of parentheses

6x^2+10x-3x-5-180=0

We add all the numbers together, and all the variables

6x^2+7x-185=0

a = 6; b = 7; c = -185;
Δ = b2-4ac
Δ = 72-4·6·(-185)
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-67}{2*6}=\frac{-74}{12}
=-6+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+67}{2*6}=\frac{60}{12}
=5
$