(2x+22)(3x-2)=90

Solution for (2x+22)(3x-2)=90 equation:

(2x+22)(3x-2)=90

We move all terms to the left:

(2x+22)(3x-2)-(90)=0

We multiply parentheses ..

(+6x^2-4x+66x-44)-90=0

We get rid of parentheses

6x^2-4x+66x-44-90=0

We add all the numbers together, and all the variables

6x^2+62x-134=0

a = 6; b = 62; c = -134;
Δ = b2-4ac
Δ = 622-4·6·(-134)
Δ = 7060
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:

$\sqrt{\Delta}=\sqrt{7060}=\sqrt{4*1765}=\sqrt{4}*\sqrt{1765}=2\sqrt{1765}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{1765}}{2*6}=\frac{-62-2\sqrt{1765}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{1765}}{2*6}=\frac{-62+2\sqrt{1765}}{12}
$