2(2x+5)x=-2

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

2(2x+5)x=-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

4x^2+10x+2=0

a = 4; b = 10; c = +2;
Δ = b2-4ac
Δ = 102-4·4·2
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{17}}{2*4}=\frac{-10-2\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{17}}{2*4}=\frac{-10+2\sqrt{17}}{8}
$