Y=x^2-10x-16

Solution for Y=x^2-10x-16 equation:

=Y^2-10Y-16

We move all terms to the left:

-(Y^2-10Y-16)=0

We get rid of parentheses

-Y^2+10Y+16=0

We add all the numbers together, and all the variables

-1Y^2+10Y+16=0

a = -1; b = 10; c = +16;
Δ = b2-4ac
Δ = 102-4·(-1)·16
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{41}}{2*-1}=\frac{-10-2\sqrt{41}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{41}}{2*-1}=\frac{-10+2\sqrt{41}}{-2}
$