(3x+17)(9x-2)=180

Solution for (3x+17)(9x-2)=180 equation:

(3x+17)(9x-2)=180

We move all terms to the left:

(3x+17)(9x-2)-(180)=0

We multiply parentheses ..

(+27x^2-6x+153x-34)-180=0

We get rid of parentheses

27x^2-6x+153x-34-180=0

We add all the numbers together, and all the variables

27x^2+147x-214=0

a = 27; b = 147; c = -214;
Δ = b2-4ac
Δ = 1472-4·27·(-214)
Δ = 44721
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:

$\sqrt{\Delta}=\sqrt{44721}=\sqrt{9*4969}=\sqrt{9}*\sqrt{4969}=3\sqrt{4969}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(147)-3\sqrt{4969}}{2*27}=\frac{-147-3\sqrt{4969}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(147)+3\sqrt{4969}}{2*27}=\frac{-147+3\sqrt{4969}}{54}
$