19x^2=-13x

Solution for 19x^2=-13x equation:

19x^2=-13x

We move all terms to the left:

19x^2-(-13x)=0

We get rid of parentheses

19x^2+13x=0

a = 19; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·19·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*19}=\frac{-26}{38}
=-13/19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*19}=\frac{0}{38}
=0
$