Y=5x2+6x+1

Solution for Y=5x2+6x+1 equation:

=5Y^2+6Y+1

We move all terms to the left:

-(5Y^2+6Y+1)=0

We get rid of parentheses

-5Y^2-6Y-1=0

a = -5; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·(-5)·(-1)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*-5}=\frac{2}{-10}
=-1/5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*-5}=\frac{10}{-10}
=-1
$