1/7x+x=32

Solution for 1/7x+x=32 equation:

1/7x+x=32

We move all terms to the left:

1/7x+x-(32)=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+1/7x-32=0

We multiply all the terms by the denominator


x*7x-32*7x+1=0

Wy multiply elements

7x^2-224x+1=0

a = 7; b = -224; c = +1;
Δ = b2-4ac
Δ = -2242-4·7·1
Δ = 50148
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:

$\sqrt{\Delta}=\sqrt{50148}=\sqrt{36*1393}=\sqrt{36}*\sqrt{1393}=6\sqrt{1393}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-224)-6\sqrt{1393}}{2*7}=\frac{224-6\sqrt{1393}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-224)+6\sqrt{1393}}{2*7}=\frac{224+6\sqrt{1393}}{14}
$