(2x+17)(3x-4)=180

Solution for (2x+17)(3x-4)=180 equation:

(2x+17)(3x-4)=180

We move all terms to the left:

(2x+17)(3x-4)-(180)=0

We multiply parentheses ..

(+6x^2-8x+51x-68)-180=0

We get rid of parentheses

6x^2-8x+51x-68-180=0

We add all the numbers together, and all the variables

6x^2+43x-248=0

a = 6; b = 43; c = -248;
Δ = b2-4ac
Δ = 432-4·6·(-248)
Δ = 7801
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{-(43)-\sqrt{7801}}{2*6}=\frac{-43-\sqrt{7801}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+\sqrt{7801}}{2*6}=\frac{-43+\sqrt{7801}}{12}
$