Y=x^2-14x+39

Solution for Y=x^2-14x+39 equation:

=Y^2-14Y+39

We move all terms to the left:

-(Y^2-14Y+39)=0

We get rid of parentheses

-Y^2+14Y-39=0

We add all the numbers together, and all the variables

-1Y^2+14Y-39=0

a = -1; b = 14; c = -39;
Δ = b2-4ac
Δ = 142-4·(-1)·(-39)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{10}}{2*-1}=\frac{-14-2\sqrt{10}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{10}}{2*-1}=\frac{-14+2\sqrt{10}}{-2}
$