X-24=13-28/x

Solution for X-24=13-28/x equation:

X-24=13-28/X

We move all terms to the left:

X-24-(13-28/X)=0


Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(-28/X+13)-24=0

We get rid of parentheses

X+28/X-13-24=0

We multiply all the terms by the denominator


X*X-13*X-24*X+28=0

We add all the numbers together, and all the variables

-37X+X*X+28=0

Wy multiply elements

X^2-37X+28=0

a = 1; b = -37; c = +28;
Δ = b2-4ac
Δ = -372-4·1·28
Δ = 1257
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{-(-37)-\sqrt{1257}}{2*1}=\frac{37-\sqrt{1257}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{1257}}{2*1}=\frac{37+\sqrt{1257}}{2}
$