Y=5x2-3x-1

Solution for Y=5x2-3x-1 equation:

=5Y^2-3Y-1

We move all terms to the left:

-(5Y^2-3Y-1)=0

We get rid of parentheses

-5Y^2+3Y+1=0

a = -5; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-5)·1
Δ = 29
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{-(3)-\sqrt{29}}{2*-5}=\frac{-3-\sqrt{29}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{29}}{2*-5}=\frac{-3+\sqrt{29}}{-10}
$