Y=10x2-2+x

Solution for Y=10x2-2+x equation:

=10Y^2-2+Y

We move all terms to the left:

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

We get rid of parentheses

-10Y^2-Y+2=0

We add all the numbers together, and all the variables

-10Y^2-1Y+2=0

a = -10; b = -1; c = +2;
Δ = b2-4ac
Δ = -12-4·(-10)·2
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*-10}=\frac{-8}{-20}
=2/5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*-10}=\frac{10}{-20}
=-1/2
$