19y^2-13y+2=-y^2

Solution for 19y^2-13y+2=-y^2 equation:

19y^2-13y+2=-y^2

We move all terms to the left:

19y^2-13y+2-(-y^2)=0

We get rid of parentheses

19y^2+y^2-13y+2=0

We add all the numbers together, and all the variables

20y^2-13y+2=0

a = 20; b = -13; c = +2;
Δ = b2-4ac
Δ = -132-4·20·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3}{2*20}=\frac{10}{40}
=1/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3}{2*20}=\frac{16}{40}
=2/5
$