(2x+39)(9x-37)=90

Solution for (2x+39)(9x-37)=90 equation:

(2x+39)(9x-37)=90

We move all terms to the left:

(2x+39)(9x-37)-(90)=0

We multiply parentheses ..

(+18x^2-74x+351x-1443)-90=0

We get rid of parentheses

18x^2-74x+351x-1443-90=0

We add all the numbers together, and all the variables

18x^2+277x-1533=0

a = 18; b = 277; c = -1533;
Δ = b2-4ac
Δ = 2772-4·18·(-1533)
Δ = 187105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(277)-\sqrt{187105}}{2*18}=\frac{-277-\sqrt{187105}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(277)+\sqrt{187105}}{2*18}=\frac{-277+\sqrt{187105}}{36}
$