5x+25=x^2

Solution for 5x+25=x^2 equation:

5x+25=x^2

We move all terms to the left:

5x+25-(x^2)=0

determiningTheFunctionDomain
-x^2+5x+25=0

We add all the numbers together, and all the variables

-1x^2+5x+25=0

a = -1; b = 5; c = +25;
Δ = b2-4ac
Δ = 52-4·(-1)·25
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{5}}{2*-1}=\frac{-5-5\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{5}}{2*-1}=\frac{-5+5\sqrt{5}}{-2}
$