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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x-5x(x+2)+7=0

We multiply parentheses

-5x^2+2x-10x+7=0

We add all the numbers together, and all the variables

-5x^2-8x+7=0

a = -5; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·(-5)·7
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{51}}{2*-5}=\frac{8-2\sqrt{51}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{51}}{2*-5}=\frac{8+2\sqrt{51}}{-10}
$