(2x+13)(8x-41)=180

Solution for (2x+13)(8x-41)=180 equation:

(2x+13)(8x-41)=180

We move all terms to the left:

(2x+13)(8x-41)-(180)=0

We multiply parentheses ..

(+16x^2-82x+104x-533)-180=0

We get rid of parentheses

16x^2-82x+104x-533-180=0

We add all the numbers together, and all the variables

16x^2+22x-713=0

a = 16; b = 22; c = -713;
Δ = b2-4ac
Δ = 222-4·16·(-713)
Δ = 46116
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:

$\sqrt{\Delta}=\sqrt{46116}=\sqrt{36*1281}=\sqrt{36}*\sqrt{1281}=6\sqrt{1281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-6\sqrt{1281}}{2*16}=\frac{-22-6\sqrt{1281}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+6\sqrt{1281}}{2*16}=\frac{-22+6\sqrt{1281}}{32}
$