3y^2=13y-14

Solution for 3y^2=13y-14 equation:

3y^2=13y-14

We move all terms to the left:

3y^2-(13y-14)=0

We get rid of parentheses

3y^2-13y+14=0

a = 3; b = -13; c = +14;
Δ = b2-4ac
Δ = -132-4·3·14
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{-(-13)-1}{2*3}=\frac{12}{6}
=2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+1}{2*3}=\frac{14}{6}
=2+1/3
$