Y=X^2-2x-49

Solution for Y=X^2-2x-49 equation:

=Y^2-2Y-49

We move all terms to the left:

-(Y^2-2Y-49)=0

We get rid of parentheses

-Y^2+2Y+49=0

We add all the numbers together, and all the variables

-1Y^2+2Y+49=0

a = -1; b = 2; c = +49;
Δ = b2-4ac
Δ = 22-4·(-1)·49
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10\sqrt{2}}{2*-1}=\frac{-2-10\sqrt{2}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10\sqrt{2}}{2*-1}=\frac{-2+10\sqrt{2}}{-2}
$