(2x+11)(2x+5)=50

Solution for (2x+11)(2x+5)=50 equation:

(2x+11)(2x+5)=50

We move all terms to the left:

(2x+11)(2x+5)-(50)=0

We multiply parentheses ..

(+4x^2+10x+22x+55)-50=0

We get rid of parentheses

4x^2+10x+22x+55-50=0

We add all the numbers together, and all the variables

4x^2+32x+5=0

a = 4; b = 32; c = +5;
Δ = b2-4ac
Δ = 322-4·4·5
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{59}}{2*4}=\frac{-32-4\sqrt{59}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{59}}{2*4}=\frac{-32+4\sqrt{59}}{8}
$