x=1/6x+14

Solution for x=1/6x+14 equation:

x=1/6x+14

We move all terms to the left:

x-(1/6x+14)=0


Domain of the equation: 6x+14)!=0

x∈R


We get rid of parentheses

x-1/6x-14=0

We multiply all the terms by the denominator


x*6x-14*6x-1=0

Wy multiply elements

6x^2-84x-1=0

a = 6; b = -84; c = -1;
Δ = b2-4ac
Δ = -842-4·6·(-1)
Δ = 7080
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:

$\sqrt{\Delta}=\sqrt{7080}=\sqrt{4*1770}=\sqrt{4}*\sqrt{1770}=2\sqrt{1770}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1770}}{2*6}=\frac{84-2\sqrt{1770}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1770}}{2*6}=\frac{84+2\sqrt{1770}}{12}
$