Y=5x2+9x-2

Solution for Y=5x2+9x-2 equation:

=5Y^2+9Y-2

We move all terms to the left:

-(5Y^2+9Y-2)=0

We get rid of parentheses

-5Y^2-9Y+2=0

a = -5; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·(-5)·2
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-11}{2*-5}=\frac{-2}{-10}
=1/5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+11}{2*-5}=\frac{20}{-10}
=-2
$