(3x-17)(8x+10)=180

Solution for (3x-17)(8x+10)=180 equation:

(3x-17)(8x+10)=180

We move all terms to the left:

(3x-17)(8x+10)-(180)=0

We multiply parentheses ..

(+24x^2+30x-136x-170)-180=0

We get rid of parentheses

24x^2+30x-136x-170-180=0

We add all the numbers together, and all the variables

24x^2-106x-350=0

a = 24; b = -106; c = -350;
Δ = b2-4ac
Δ = -1062-4·24·(-350)
Δ = 44836
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:

$\sqrt{\Delta}=\sqrt{44836}=\sqrt{4*11209}=\sqrt{4}*\sqrt{11209}=2\sqrt{11209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106)-2\sqrt{11209}}{2*24}=\frac{106-2\sqrt{11209}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106)+2\sqrt{11209}}{2*24}=\frac{106+2\sqrt{11209}}{48}
$