X(0.25x)=x+13

Solution for X(0.25x)=x+13 equation:

X(0.25X)=X+13

We move all terms to the left:

X(0.25X)-(X+13)=0

We add all the numbers together, and all the variables

X(+0.25X)-(X+13)=0

We multiply parentheses

0X^2-(X+13)=0

We get rid of parentheses

0X^2-X-13=0

We add all the numbers together, and all the variables

X^2-1X-13=0

a = 1; b = -1; c = -13;
Δ = b2-4ac
Δ = -12-4·1·(-13)
Δ = 53
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{53}}{2*1}=\frac{1-\sqrt{53}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{53}}{2*1}=\frac{1+\sqrt{53}}{2}
$