(x)(x+6)=(25)(x)

Solution for (x)(x+6)=(25)(x) equation:

(x)(x+6)=(25)(x)

We move all terms to the left:

(x)(x+6)-((25)(x))=0

determiningTheFunctionDomain
x(x+6)-25x=0

We add all the numbers together, and all the variables

-25x+x(x+6)=0

We multiply parentheses

x^2-25x+6x=0

We add all the numbers together, and all the variables

x^2-19x=0

a = 1; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·1·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*1}=\frac{38}{2}
=19
$