6y^2-5=-y

Solution for 6y^2-5=-y equation:

6y^2-5=-y

We move all terms to the left:

6y^2-5-(-y)=0

We add all the numbers together, and all the variables

6y^2-(-1y)-5=0

We get rid of parentheses

6y^2+1y-5=0

We add all the numbers together, and all the variables

6y^2+y-5=0

a = 6; b = 1; c = -5;
Δ = b2-4ac
Δ = 12-4·6·(-5)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*6}=\frac{-12}{12}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*6}=\frac{10}{12}
=5/6
$