2y^2-y=9

Solution for 2y^2-y=9 equation:

2y^2-y=9

We move all terms to the left:

2y^2-y-(9)=0

We add all the numbers together, and all the variables

2y^2-1y-9=0

a = 2; b = -1; c = -9;
Δ = b2-4ac
Δ = -12-4·2·(-9)
Δ = 73
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{73}}{2*2}=\frac{1-\sqrt{73}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{73}}{2*2}=\frac{1+\sqrt{73}}{4}
$