4y^2-y=11

Solution for 4y^2-y=11 equation:

4y^2-y=11

We move all terms to the left:

4y^2-y-(11)=0

We add all the numbers together, and all the variables

4y^2-1y-11=0

a = 4; b = -1; c = -11;
Δ = b2-4ac
Δ = -12-4·4·(-11)
Δ = 177
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{-(-1)-\sqrt{177}}{2*4}=\frac{1-\sqrt{177}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{177}}{2*4}=\frac{1+\sqrt{177}}{8}
$