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

Solution for -5x(x+2)-2x=4x-14 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-5x^2-2x-10x-(4x-14)=0

We get rid of parentheses

-5x^2-2x-10x-4x+14=0

We add all the numbers together, and all the variables

-5x^2-16x+14=0

a = -5; b = -16; c = +14;
Δ = b2-4ac
Δ = -162-4·(-5)·14
Δ = 536
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:

$\sqrt{\Delta}=\sqrt{536}=\sqrt{4*134}=\sqrt{4}*\sqrt{134}=2\sqrt{134}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{134}}{2*-5}=\frac{16-2\sqrt{134}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{134}}{2*-5}=\frac{16+2\sqrt{134}}{-10}
$