5x-42/x-8=x

Solution for 5x-42/x-8=x equation:

5x-42/x-8=x

We move all terms to the left:

5x-42/x-8-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x-42/x-8=0

We multiply all the terms by the denominator


4x*x-8*x-42=0

We add all the numbers together, and all the variables

-8x+4x*x-42=0

Wy multiply elements

4x^2-8x-42=0

a = 4; b = -8; c = -42;
Δ = b2-4ac
Δ = -82-4·4·(-42)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{46}}{2*4}=\frac{8-4\sqrt{46}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{46}}{2*4}=\frac{8+4\sqrt{46}}{8}
$