Y=3x2+5x-1

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

=3Y^2+5Y-1

We move all terms to the left:

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

We get rid of parentheses

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

a = -3; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·(-3)·1
Δ = 37
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{37}}{2*-3}=\frac{5-\sqrt{37}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{37}}{2*-3}=\frac{5+\sqrt{37}}{-6}
$