X-4/x=15/x-4

Solution for X-4/x=15/x-4 equation:

X-4/X=15/X-4

We move all terms to the left:

X-4/X-(15/X-4)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X-4)!=0

X∈R


We get rid of parentheses

X-4/X-15/X+4=0

We multiply all the terms by the denominator


X*X+4*X-4-15=0

We add all the numbers together, and all the variables

4X+X*X-19=0

Wy multiply elements

X^2+4X-19=0

a = 1; b = 4; c = -19;
Δ = b2-4ac
Δ = 42-4·1·(-19)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{23}}{2*1}=\frac{-4-2\sqrt{23}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{23}}{2*1}=\frac{-4+2\sqrt{23}}{2}
$