6y^2=11y-5

Solution for 6y^2=11y-5 equation:

6y^2=11y-5

We move all terms to the left:

6y^2-(11y-5)=0

We get rid of parentheses

6y^2-11y+5=0

a = 6; b = -11; c = +5;
Δ = b2-4ac
Δ = -112-4·6·5
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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