25=x^2+14*x+49

Solution for 25=x^2+14*x+49 equation:

25=x^2+14x+49

We move all terms to the left:

25-(x^2+14x+49)=0

We get rid of parentheses

-x^2-14x-49+25=0

We add all the numbers together, and all the variables

-1x^2-14x-24=0

a = -1; b = -14; c = -24;
Δ = b2-4ac
Δ = -142-4·(-1)·(-24)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10}{2*-1}=\frac{4}{-2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*-1}=\frac{24}{-2}
=-12
$