(12x+-37)(9x+5)=180

Solution for (12x+-37)(9x+5)=180 equation:

(12x+-37)(9x+5)=180

We move all terms to the left:

(12x+-37)(9x+5)-(180)=0

We add all the numbers together, and all the variables

(12x-37)(9x+5)-180=0

We multiply parentheses ..

(+108x^2+60x-333x-185)-180=0

We get rid of parentheses

108x^2+60x-333x-185-180=0

We add all the numbers together, and all the variables

108x^2-273x-365=0

a = 108; b = -273; c = -365;
Δ = b2-4ac
Δ = -2732-4·108·(-365)
Δ = 232209
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:

$\sqrt{\Delta}=\sqrt{232209}=\sqrt{9*25801}=\sqrt{9}*\sqrt{25801}=3\sqrt{25801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-273)-3\sqrt{25801}}{2*108}=\frac{273-3\sqrt{25801}}{216}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-273)+3\sqrt{25801}}{2*108}=\frac{273+3\sqrt{25801}}{216}
$