(3x-9)(2x+17)=90

Solution for (3x-9)(2x+17)=90 equation:

(3x-9)(2x+17)=90

We move all terms to the left:

(3x-9)(2x+17)-(90)=0

We multiply parentheses ..

(+6x^2+51x-18x-153)-90=0

We get rid of parentheses

6x^2+51x-18x-153-90=0

We add all the numbers together, and all the variables

6x^2+33x-243=0

a = 6; b = 33; c = -243;
Δ = b2-4ac
Δ = 332-4·6·(-243)
Δ = 6921
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:

$\sqrt{\Delta}=\sqrt{6921}=\sqrt{9*769}=\sqrt{9}*\sqrt{769}=3\sqrt{769}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{769}}{2*6}=\frac{-33-3\sqrt{769}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{769}}{2*6}=\frac{-33+3\sqrt{769}}{12}
$