2y^2-11y=22

Solution for 2y^2-11y=22 equation:

2y^2-11y=22

We move all terms to the left:

2y^2-11y-(22)=0

a = 2; b = -11; c = -22;
Δ = b2-4ac
Δ = -112-4·2·(-22)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3\sqrt{33}}{2*2}=\frac{11-3\sqrt{33}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3\sqrt{33}}{2*2}=\frac{11+3\sqrt{33}}{4}
$