6y^2+5y=6

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

6y^2+5y=6

We move all terms to the left:

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

a = 6; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·6·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-13}{2*6}=\frac{-18}{12}
=-1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+13}{2*6}=\frac{8}{12}
=2/3
$