y=34y-3y^2+155

Solution for y=34y-3y^2+155 equation:

y=34y-3y^2+155

We move all terms to the left:

y-(34y-3y^2+155)=0

We get rid of parentheses

3y^2-34y+y-155=0

We add all the numbers together, and all the variables

3y^2-33y-155=0

a = 3; b = -33; c = -155;
Δ = b2-4ac
Δ = -332-4·3·(-155)
Δ = 2949
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-\sqrt{2949}}{2*3}=\frac{33-\sqrt{2949}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{2949}}{2*3}=\frac{33+\sqrt{2949}}{6}
$