(12x+-37)(9x+5)=90

Solution for (12x+-37)(9x+5)=90 equation:

(12x+-37)(9x+5)=90

We move all terms to the left:

(12x+-37)(9x+5)-(90)=0

We add all the numbers together, and all the variables

(12x-37)(9x+5)-90=0

We multiply parentheses ..

(+108x^2+60x-333x-185)-90=0

We get rid of parentheses

108x^2+60x-333x-185-90=0

We add all the numbers together, and all the variables

108x^2-273x-275=0

a = 108; b = -273; c = -275;
Δ = b2-4ac
Δ = -2732-4·108·(-275)
Δ = 193329
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:

$\sqrt{\Delta}=\sqrt{193329}=\sqrt{9*21481}=\sqrt{9}*\sqrt{21481}=3\sqrt{21481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-273)-3\sqrt{21481}}{2*108}=\frac{273-3\sqrt{21481}}{216}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-273)+3\sqrt{21481}}{2*108}=\frac{273+3\sqrt{21481}}{216}
$