4y^2-y=33

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

4y^2-y=33

We move all terms to the left:

4y^2-y-(33)=0

We add all the numbers together, and all the variables

4y^2-1y-33=0

a = 4; b = -1; c = -33;
Δ = b2-4ac
Δ = -12-4·4·(-33)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-23}{2*4}=\frac{-22}{8}
=-2+3/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+23}{2*4}=\frac{24}{8}
=3
$