c=x^2+24x+25

Solution for c=x^2+24x+25 equation:

=C^2+24C+25

We move all terms to the left:

-(C^2+24C+25)=0

We get rid of parentheses

-C^2-24C-25=0

We add all the numbers together, and all the variables

-1C^2-24C-25=0

a = -1; b = -24; c = -25;
Δ = b2-4ac
Δ = -242-4·(-1)·(-25)
Δ = 476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{476}=\sqrt{4*119}=\sqrt{4}*\sqrt{119}=2\sqrt{119}$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{119}}{2*-1}=\frac{24-2\sqrt{119}}{-2}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{119}}{2*-1}=\frac{24+2\sqrt{119}}{-2}
$