Y=x^2-10x-40

Solution for Y=x^2-10x-40 equation:

=Y^2-10Y-40

We move all terms to the left:

-(Y^2-10Y-40)=0

We get rid of parentheses

-Y^2+10Y+40=0

We add all the numbers together, and all the variables

-1Y^2+10Y+40=0

a = -1; b = 10; c = +40;
Δ = b2-4ac
Δ = 102-4·(-1)·40
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{65}}{2*-1}=\frac{-10-2\sqrt{65}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{65}}{2*-1}=\frac{-10+2\sqrt{65}}{-2}
$