x^2+25x=-5

Solution for x^2+25x=-5 equation:

x^2+25x=-5

We move all terms to the left:

x^2+25x-(-5)=0

We add all the numbers together, and all the variables

x^2+25x+5=0

a = 1; b = 25; c = +5;
Δ = b2-4ac
Δ = 252-4·1·5
Δ = 605
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:

$\sqrt{\Delta}=\sqrt{605}=\sqrt{121*5}=\sqrt{121}*\sqrt{5}=11\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-11\sqrt{5}}{2*1}=\frac{-25-11\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+11\sqrt{5}}{2*1}=\frac{-25+11\sqrt{5}}{2}
$