18y^2-13y+2=-y2

Solution for 18y^2-13y+2=-y2 equation:

18y^2-13y+2=-y2

We move all terms to the left:

18y^2-13y+2-(-y2)=0

We add all the numbers together, and all the variables

18y^2-(-1y^2)-13y+2=0

We get rid of parentheses

18y^2+1y^2-13y+2=0

We add all the numbers together, and all the variables

19y^2-13y+2=0

a = 19; b = -13; c = +2;
Δ = b2-4ac
Δ = -132-4·19·2
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{17}}{2*19}=\frac{13-\sqrt{17}}{38}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{17}}{2*19}=\frac{13+\sqrt{17}}{38}
$