Y=5x^2+6x-2

Solution for Y=5x^2+6x-2 equation:

=5Y^2+6Y-2

We move all terms to the left:

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

We get rid of parentheses

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

a = -5; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·(-5)·2
Δ = 76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{19}}{2*-5}=\frac{6-2\sqrt{19}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{19}}{2*-5}=\frac{6+2\sqrt{19}}{-10}
$