1/7x=x-18

Solution for 1/7x=x-18 equation:

1/7x=x-18

We move all terms to the left:

1/7x-(x-18)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

1/7x-x+18=0

We multiply all the terms by the denominator


-x*7x+18*7x+1=0

Wy multiply elements

-7x^2+126x+1=0

a = -7; b = 126; c = +1;
Δ = b2-4ac
Δ = 1262-4·(-7)·1
Δ = 15904
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:

$\sqrt{\Delta}=\sqrt{15904}=\sqrt{16*994}=\sqrt{16}*\sqrt{994}=4\sqrt{994}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-4\sqrt{994}}{2*-7}=\frac{-126-4\sqrt{994}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+4\sqrt{994}}{2*-7}=\frac{-126+4\sqrt{994}}{-14}
$