6y2+5=-13y

Solution for 6y2+5=-13y equation:

6y^2+5=-13y

We move all terms to the left:

6y^2+5-(-13y)=0

We get rid of parentheses

6y^2+13y+5=0

a = 6; b = 13; c = +5;
Δ = b2-4ac
Δ = 132-4·6·5
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-7}{2*6}=\frac{-20}{12}
=-1+2/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*6}=\frac{-6}{12}
=-1/2
$