Y=2x2+5x-1

Solution for Y=2x2+5x-1 equation:

=2Y^2+5Y-1

We move all terms to the left:

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

We get rid of parentheses

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

a = -2; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·(-2)·1
Δ = 33
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{-(-5)-\sqrt{33}}{2*-2}=\frac{5-\sqrt{33}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{33}}{2*-2}=\frac{5+\sqrt{33}}{-4}
$