7x^2=-7x

Solution for 7x^2=-7x equation:

7x^2=-7x

We move all terms to the left:

7x^2-(-7x)=0

We get rid of parentheses

7x^2+7x=0

a = 7; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·7·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*7}=\frac{-14}{14}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*7}=\frac{0}{14}
=0
$