Y=2x^2+x-5

Solution for Y=2x^2+x-5 equation:

=2Y^2+Y-5

We move all terms to the left:

-(2Y^2+Y-5)=0

We get rid of parentheses

-2Y^2-Y+5=0

We add all the numbers together, and all the variables

-2Y^2-1Y+5=0

a = -2; b = -1; c = +5;
Δ = b2-4ac
Δ = -12-4·(-2)·5
Δ = 41
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{41}}{2*-2}=\frac{1-\sqrt{41}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{41}}{2*-2}=\frac{1+\sqrt{41}}{-4}
$