15y^2=6+13y

Solution for 15y^2=6+13y equation:

15y^2=6+13y

We move all terms to the left:

15y^2-(6+13y)=0

We add all the numbers together, and all the variables

15y^2-(13y+6)=0

We get rid of parentheses

15y^2-13y-6=0

a = 15; b = -13; c = -6;
Δ = b2-4ac
Δ = -132-4·15·(-6)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-23}{2*15}=\frac{-10}{30}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+23}{2*15}=\frac{36}{30}
=1+1/5
$