-4x(2x+5)+2x+3=-11

Solution for -4x(2x+5)+2x+3=-11 equation:

-4x(2x+5)+2x+3=-11

We move all terms to the left:

-4x(2x+5)+2x+3-(-11)=0

We add all the numbers together, and all the variables

2x-4x(2x+5)+14=0

We multiply parentheses

-8x^2+2x-20x+14=0

We add all the numbers together, and all the variables

-8x^2-18x+14=0

a = -8; b = -18; c = +14;
Δ = b2-4ac
Δ = -182-4·(-8)·14
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{193}}{2*-8}=\frac{18-2\sqrt{193}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{193}}{2*-8}=\frac{18+2\sqrt{193}}{-16}
$