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

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

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

We move all terms to the left:

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

We multiply parentheses

-4x^2-20x-(2(x+11))=0


We calculate terms in parentheses: -(2(x+11)), so:

2(x+11)

We multiply parentheses

2x+22

Back to the equation:

-(2x+22)


We get rid of parentheses

-4x^2-20x-2x-22=0

We add all the numbers together, and all the variables

-4x^2-22x-22=0

a = -4; b = -22; c = -22;
Δ = b2-4ac
Δ = -222-4·(-4)·(-22)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{33}}{2*-4}=\frac{22-2\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{33}}{2*-4}=\frac{22+2\sqrt{33}}{-8}
$