2y^2-y=200

Solution for 2y^2-y=200 equation:

2y^2-y=200

We move all terms to the left:

2y^2-y-(200)=0

We add all the numbers together, and all the variables

2y^2-1y-200=0

a = 2; b = -1; c = -200;
Δ = b2-4ac
Δ = -12-4·2·(-200)
Δ = 1601
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{1601}}{2*2}=\frac{1-\sqrt{1601}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1601}}{2*2}=\frac{1+\sqrt{1601}}{4}
$