Y=10y2+9y+2

Solution for Y=10y2+9y+2 equation:

=10Y^2+9Y+2

We move all terms to the left:

-(10Y^2+9Y+2)=0

We get rid of parentheses

-10Y^2-9Y-2=0

a = -10; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·(-10)·(-2)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-1}{2*-10}=\frac{8}{-20}
=-2/5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*-10}=\frac{10}{-20}
=-1/2
$