1/7x-3x=8

Solution for 1/7x-3x=8 equation:

1/7x-3x=8

We move all terms to the left:

1/7x-3x-(8)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+1/7x-8=0

We multiply all the terms by the denominator


-3x*7x-8*7x+1=0

Wy multiply elements

-21x^2-56x+1=0

a = -21; b = -56; c = +1;
Δ = b2-4ac
Δ = -562-4·(-21)·1
Δ = 3220
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:

$\sqrt{\Delta}=\sqrt{3220}=\sqrt{4*805}=\sqrt{4}*\sqrt{805}=2\sqrt{805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{805}}{2*-21}=\frac{56-2\sqrt{805}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{805}}{2*-21}=\frac{56+2\sqrt{805}}{-42}
$