6y^2=5y+50

Solution for 6y^2=5y+50 equation:

6y^2=5y+50

We move all terms to the left:

6y^2-(5y+50)=0

We get rid of parentheses

6y^2-5y-50=0

a = 6; b = -5; c = -50;
Δ = b2-4ac
Δ = -52-4·6·(-50)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-35}{2*6}=\frac{-30}{12}
=-2+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+35}{2*6}=\frac{40}{12}
=3+1/3
$