-4x(x+2)+2x=5x+6

Solution for -4x(x+2)+2x=5x+6 equation:

-4x(x+2)+2x=5x+6

We move all terms to the left:

-4x(x+2)+2x-(5x+6)=0

We add all the numbers together, and all the variables

2x-4x(x+2)-(5x+6)=0

We multiply parentheses

-4x^2+2x-8x-(5x+6)=0

We get rid of parentheses

-4x^2+2x-8x-5x-6=0

We add all the numbers together, and all the variables

-4x^2-11x-6=0

a = -4; b = -11; c = -6;
Δ = b2-4ac
Δ = -112-4·(-4)·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*-4}=\frac{6}{-8}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*-4}=\frac{16}{-8}
=-2
$