(2x+11)(4x-5)+x=180

Solution for (2x+11)(4x-5)+x=180 equation:

(2x+11)(4x-5)+x=180

We move all terms to the left:

(2x+11)(4x-5)+x-(180)=0

We add all the numbers together, and all the variables

x+(2x+11)(4x-5)-180=0

We multiply parentheses ..

(+8x^2-10x+44x-55)+x-180=0

We get rid of parentheses

8x^2-10x+44x+x-55-180=0

We add all the numbers together, and all the variables

8x^2+35x-235=0

a = 8; b = 35; c = -235;
Δ = b2-4ac
Δ = 352-4·8·(-235)
Δ = 8745
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{-(35)-\sqrt{8745}}{2*8}=\frac{-35-\sqrt{8745}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{8745}}{2*8}=\frac{-35+\sqrt{8745}}{16}
$