3y^2=19y-26

Solution for 3y^2=19y-26 equation:

3y^2=19y-26

We move all terms to the left:

3y^2-(19y-26)=0

We get rid of parentheses

3y^2-19y+26=0

a = 3; b = -19; c = +26;
Δ = b2-4ac
Δ = -192-4·3·26
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-7}{2*3}=\frac{12}{6}
=2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+7}{2*3}=\frac{26}{6}
=4+1/3
$