Y=4x2+x-1

Solution for Y=4x2+x-1 equation:

=4Y^2+Y-1

We move all terms to the left:

-(4Y^2+Y-1)=0

We get rid of parentheses

-4Y^2-Y+1=0

We add all the numbers together, and all the variables

-4Y^2-1Y+1=0

a = -4; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-4)·1
Δ = 17
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{17}}{2*-4}=\frac{1-\sqrt{17}}{-8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{17}}{2*-4}=\frac{1+\sqrt{17}}{-8}
$