Y=x2+x-10

Solution for Y=x2+x-10 equation:

=Y2+Y-10

We move all terms to the left:

-(Y2+Y-10)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-Y^2-Y+10=0

We add all the numbers together, and all the variables

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

a = -1; b = -1; c = +10;
Δ = b2-4ac
Δ = -12-4·(-1)·10
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{41}}{2*-1}=\frac{1-\sqrt{41}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{41}}{2*-1}=\frac{1+\sqrt{41}}{-2}
$