21y^2+11y-2=y

Solution for 21y^2+11y-2=y equation:

21y^2+11y-2=y

We move all terms to the left:

21y^2+11y-2-(y)=0

We add all the numbers together, and all the variables

21y^2+10y-2=0

a = 21; b = 10; c = -2;
Δ = b2-4ac
Δ = 102-4·21·(-2)
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{67}}{2*21}=\frac{-10-2\sqrt{67}}{42}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{67}}{2*21}=\frac{-10+2\sqrt{67}}{42}
$