(2x+17)(3x+7)=180

Solution for (2x+17)(3x+7)=180 equation:

(2x+17)(3x+7)=180

We move all terms to the left:

(2x+17)(3x+7)-(180)=0

We multiply parentheses ..

(+6x^2+14x+51x+119)-180=0

We get rid of parentheses

6x^2+14x+51x+119-180=0

We add all the numbers together, and all the variables

6x^2+65x-61=0

a = 6; b = 65; c = -61;
Δ = b2-4ac
Δ = 652-4·6·(-61)
Δ = 5689
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{-(65)-\sqrt{5689}}{2*6}=\frac{-65-\sqrt{5689}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{5689}}{2*6}=\frac{-65+\sqrt{5689}}{12}
$