1/5x-3=x

Solution for 1/5x-3=x equation:

1/5x-3=x

We move all terms to the left:

1/5x-3-(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+1/5x-3=0

We multiply all the terms by the denominator


-1x*5x-3*5x+1=0

Wy multiply elements

-5x^2-15x+1=0

a = -5; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·(-5)·1
Δ = 245
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:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-7\sqrt{5}}{2*-5}=\frac{15-7\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+7\sqrt{5}}{2*-5}=\frac{15+7\sqrt{5}}{-10}
$