x=1/6x+7

Solution for x=1/6x+7 equation:

x=1/6x+7

We move all terms to the left:

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


Domain of the equation: 6x+7)!=0

x∈R


We get rid of parentheses

x-1/6x-7=0

We multiply all the terms by the denominator


x*6x-7*6x-1=0

Wy multiply elements

6x^2-42x-1=0

a = 6; b = -42; c = -1;
Δ = b2-4ac
Δ = -422-4·6·(-1)
Δ = 1788
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:

$\sqrt{\Delta}=\sqrt{1788}=\sqrt{4*447}=\sqrt{4}*\sqrt{447}=2\sqrt{447}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{447}}{2*6}=\frac{42-2\sqrt{447}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{447}}{2*6}=\frac{42+2\sqrt{447}}{12}
$