37=3y^2-2y+21

Solution for 37=3y^2-2y+21 equation:

37=3y^2-2y+21

We move all terms to the left:

37-(3y^2-2y+21)=0

We get rid of parentheses

-3y^2+2y-21+37=0

We add all the numbers together, and all the variables

-3y^2+2y+16=0

a = -3; b = 2; c = +16;
Δ = b2-4ac
Δ = 22-4·(-3)·16
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*-3}=\frac{-16}{-6}
=2+2/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*-3}=\frac{12}{-6}
=-2
$