5y^2-33y=52=0

Solution for 5y^2-33y=52=0 equation:

5y^2-33y=52=0

We move all terms to the left:

5y^2-33y-(52)=0

a = 5; b = -33; c = -52;
Δ = b2-4ac
Δ = -332-4·5·(-52)
Δ = 2129
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{2129}}{2*5}=\frac{33-\sqrt{2129}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{2129}}{2*5}=\frac{33+\sqrt{2129}}{10}
$