(1/7)x+(1/3)x=6/7

Solution for (1/7)x+(1/3)x=6/7 equation:

(1/7)x+(1/3)x=6/7

We move all terms to the left:

(1/7)x+(1/3)x-(6/7)=0


Domain of the equation: 7)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/7)x+(+1/3)x-(+6/7)=0

We multiply parentheses

x^2+x^2-(+6/7)=0

We get rid of parentheses

x^2+x^2-6/7=0

We multiply all the terms by the denominator


x^2*7+x^2*7-6=0

Wy multiply elements

7x^2+7x^2-6=0

We add all the numbers together, and all the variables

14x^2-6=0

a = 14; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·14·(-6)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{21}}{2*14}=\frac{0-4\sqrt{21}}{28}
=-\frac{4\sqrt{21}}{28}
=-\frac{\sqrt{21}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{21}}{2*14}=\frac{0+4\sqrt{21}}{28}
=\frac{4\sqrt{21}}{28}
=\frac{\sqrt{21}}{7}
$