34y-3y^2+155=0

Solution for 34y-3y^2+155=0 equation:

34y-3y^2+155=0

a = -3; b = 34; c = +155;
Δ = b2-4ac
Δ = 342-4·(-3)·155
Δ = 3016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3016}=\sqrt{4*754}=\sqrt{4}*\sqrt{754}=2\sqrt{754}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{754}}{2*-3}=\frac{-34-2\sqrt{754}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{754}}{2*-3}=\frac{-34+2\sqrt{754}}{-6}
$