x^2=-26x

Solution for x^2=-26x equation:

x^2=-26x

We move all terms to the left:

x^2-(-26x)=0

We get rid of parentheses

x^2+26x=0

a = 1; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·1·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*1}=\frac{-52}{2}
=-26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*1}=\frac{0}{2}
=0
$