(8x+17)(5x-6)=180

Solution for (8x+17)(5x-6)=180 equation:

(8x+17)(5x-6)=180

We move all terms to the left:

(8x+17)(5x-6)-(180)=0

We multiply parentheses ..

(+40x^2-48x+85x-102)-180=0

We get rid of parentheses

40x^2-48x+85x-102-180=0

We add all the numbers together, and all the variables

40x^2+37x-282=0

a = 40; b = 37; c = -282;
Δ = b2-4ac
Δ = 372-4·40·(-282)
Δ = 46489
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{-(37)-\sqrt{46489}}{2*40}=\frac{-37-\sqrt{46489}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{46489}}{2*40}=\frac{-37+\sqrt{46489}}{80}
$