5x-22-15/x-5=x

Solution for 5x-22-15/x-5=x equation:

5x-22-15/x-5=x

We move all terms to the left:

5x-22-15/x-5-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x-15/x-27=0

We multiply all the terms by the denominator


4x*x-27*x-15=0

We add all the numbers together, and all the variables

-27x+4x*x-15=0

Wy multiply elements

4x^2-27x-15=0

a = 4; b = -27; c = -15;
Δ = b2-4ac
Δ = -272-4·4·(-15)
Δ = 969
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{-(-27)-\sqrt{969}}{2*4}=\frac{27-\sqrt{969}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{969}}{2*4}=\frac{27+\sqrt{969}}{8}
$