10-1-x/5x=x

Solution for 10-1-x/5x=x equation:

10-1-x/5x=x

We move all terms to the left:

10-1-x/5x-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x-x/5x+9=0

We multiply all the terms by the denominator


-1x*5x-x+9*5x=0

We add all the numbers together, and all the variables

-1x-1x*5x+9*5x=0

Wy multiply elements

-5x^2-1x+45x=0

We add all the numbers together, and all the variables

-5x^2+44x=0

a = -5; b = 44; c = 0;
Δ = b2-4ac
Δ = 442-4·(-5)·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-44}{2*-5}=\frac{-88}{-10}
=8+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+44}{2*-5}=\frac{0}{-10}
=0
$