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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-4(2x+5)x+13=0

We multiply parentheses

-8x^2-20x+13=0

a = -8; b = -20; c = +13;
Δ = b2-4ac
Δ = -202-4·(-8)·13
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{51}}{2*-8}=\frac{20-4\sqrt{51}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{51}}{2*-8}=\frac{20+4\sqrt{51}}{-16}
$