(2x+1)(8x-17)=180

Solution for (2x+1)(8x-17)=180 equation:

(2x+1)(8x-17)=180

We move all terms to the left:

(2x+1)(8x-17)-(180)=0

We multiply parentheses ..

(+16x^2-34x+8x-17)-180=0

We get rid of parentheses

16x^2-34x+8x-17-180=0

We add all the numbers together, and all the variables

16x^2-26x-197=0

a = 16; b = -26; c = -197;
Δ = b2-4ac
Δ = -262-4·16·(-197)
Δ = 13284
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:

$\sqrt{\Delta}=\sqrt{13284}=\sqrt{324*41}=\sqrt{324}*\sqrt{41}=18\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-18\sqrt{41}}{2*16}=\frac{26-18\sqrt{41}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+18\sqrt{41}}{2*16}=\frac{26+18\sqrt{41}}{32}
$