x^2+25x=-6

Solution for x^2+25x=-6 equation:

x^2+25x=-6

We move all terms to the left:

x^2+25x-(-6)=0

We add all the numbers together, and all the variables

x^2+25x+6=0

a = 1; b = 25; c = +6;
Δ = b2-4ac
Δ = 252-4·1·6
Δ = 601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{601}}{2*1}=\frac{-25-\sqrt{601}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{601}}{2*1}=\frac{-25+\sqrt{601}}{2}
$