Y=4x^2-3x-1

Solution for Y=4x^2-3x-1 equation:

=4Y^2-3Y-1

We move all terms to the left:

-(4Y^2-3Y-1)=0

We get rid of parentheses

-4Y^2+3Y+1=0

a = -4; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-4)·1
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5}{2*-4}=\frac{-8}{-8}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5}{2*-4}=\frac{2}{-8}
=-1/4
$