68=1/5x-x

Solution for 68=1/5x-x equation:

68=1/5x-x

We move all terms to the left:

68-(1/5x-x)=0


Domain of the equation: 5x-x)!=0

x∈R


We add all the numbers together, and all the variables

-(-1x+1/5x)+68=0

We get rid of parentheses

1x-1/5x+68=0

We multiply all the terms by the denominator


1x*5x+68*5x-1=0

Wy multiply elements

5x^2+340x-1=0

a = 5; b = 340; c = -1;
Δ = b2-4ac
Δ = 3402-4·5·(-1)
Δ = 115620
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:

$\sqrt{\Delta}=\sqrt{115620}=\sqrt{4*28905}=\sqrt{4}*\sqrt{28905}=2\sqrt{28905}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(340)-2\sqrt{28905}}{2*5}=\frac{-340-2\sqrt{28905}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(340)+2\sqrt{28905}}{2*5}=\frac{-340+2\sqrt{28905}}{10}
$