X-3=x^2+25x+25

Solution for X-3=x^2+25x+25 equation:

X-3=X^2+25X+25

We move all terms to the left:

X-3-(X^2+25X+25)=0

We get rid of parentheses

-X^2+X-25X-25-3=0

We add all the numbers together, and all the variables

-1X^2-24X-28=0

a = -1; b = -24; c = -28;
Δ = b2-4ac
Δ = -242-4·(-1)·(-28)
Δ = 464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{29}}{2*-1}=\frac{24-4\sqrt{29}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{29}}{2*-1}=\frac{24+4\sqrt{29}}{-2}
$