X=15/x-22

Solution for X=15/x-22 equation:

X=15/X-22

We move all terms to the left:

X-(15/X-22)=0


Domain of the equation: X-22)!=0

X∈R


We get rid of parentheses

X-15/X+22=0

We multiply all the terms by the denominator


X*X+22*X-15=0

We add all the numbers together, and all the variables

22X+X*X-15=0

Wy multiply elements

X^2+22X-15=0

a = 1; b = 22; c = -15;
Δ = b2-4ac
Δ = 222-4·1·(-15)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-4\sqrt{34}}{2*1}=\frac{-22-4\sqrt{34}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+4\sqrt{34}}{2*1}=\frac{-22+4\sqrt{34}}{2}
$