Y=x^2-14x+25

Solution for Y=x^2-14x+25 equation:

=Y^2-14Y+25

We move all terms to the left:

-(Y^2-14Y+25)=0

We get rid of parentheses

-Y^2+14Y-25=0

We add all the numbers together, and all the variables

-1Y^2+14Y-25=0

a = -1; b = 14; c = -25;
Δ = b2-4ac
Δ = 142-4·(-1)·(-25)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{6}}{2*-1}=\frac{-14-4\sqrt{6}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{6}}{2*-1}=\frac{-14+4\sqrt{6}}{-2}
$