2x(x+5)=-1

Solution for 2x(x+5)=-1 equation:

2x(x+5)=-1

We move all terms to the left:

2x(x+5)-(-1)=0

We add all the numbers together, and all the variables

2x(x+5)+1=0

We multiply parentheses

2x^2+10x+1=0

a = 2; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·2·1
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{23}}{2*2}=\frac{-10-2\sqrt{23}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{23}}{2*2}=\frac{-10+2\sqrt{23}}{4}
$