6/7x+x=52

Solution for 6/7x+x=52 equation:

6/7x+x=52

We move all terms to the left:

6/7x+x-(52)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

x+6/7x-52=0

We multiply all the terms by the denominator


x*7x-52*7x+6=0

Wy multiply elements

7x^2-364x+6=0

a = 7; b = -364; c = +6;
Δ = b2-4ac
Δ = -3642-4·7·6
Δ = 132328
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:

$\sqrt{\Delta}=\sqrt{132328}=\sqrt{4*33082}=\sqrt{4}*\sqrt{33082}=2\sqrt{33082}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-364)-2\sqrt{33082}}{2*7}=\frac{364-2\sqrt{33082}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-364)+2\sqrt{33082}}{2*7}=\frac{364+2\sqrt{33082}}{14}
$