Y=x^2+26x+50

Solution for Y=x^2+26x+50 equation:

=Y^2+26Y+50

We move all terms to the left:

-(Y^2+26Y+50)=0

We get rid of parentheses

-Y^2-26Y-50=0

We add all the numbers together, and all the variables

-1Y^2-26Y-50=0

a = -1; b = -26; c = -50;
Δ = b2-4ac
Δ = -262-4·(-1)·(-50)
Δ = 476
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:

$\sqrt{\Delta}=\sqrt{476}=\sqrt{4*119}=\sqrt{4}*\sqrt{119}=2\sqrt{119}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{119}}{2*-1}=\frac{26-2\sqrt{119}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{119}}{2*-1}=\frac{26+2\sqrt{119}}{-2}
$