5y^2-4y-33=0

Solution for 5y^2-4y-33=0 equation:

5y^2-4y-33=0

a = 5; b = -4; c = -33;
Δ = b2-4ac
Δ = -42-4·5·(-33)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-26}{2*5}=\frac{-22}{10}
=-2+1/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+26}{2*5}=\frac{30}{10}
=3
$