5x^2+10x=-1

Solution for 5x^2+10x=-1 equation:

5x^2+10x=-1

We move all terms to the left:

5x^2+10x-(-1)=0

We add all the numbers together, and all the variables

5x^2+10x+1=0

a = 5; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·5·1
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{5}}{2*5}=\frac{-10-4\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{5}}{2*5}=\frac{-10+4\sqrt{5}}{10}
$