x=14/14x+14

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

x=14/14x+14

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

x-14/14x-14=0

We multiply all the terms by the denominator


x*14x-14*14x-14=0

Wy multiply elements

14x^2-196x-14=0

a = 14; b = -196; c = -14;
Δ = b2-4ac
Δ = -1962-4·14·(-14)
Δ = 39200
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:

$\sqrt{\Delta}=\sqrt{39200}=\sqrt{19600*2}=\sqrt{19600}*\sqrt{2}=140\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-196)-140\sqrt{2}}{2*14}=\frac{196-140\sqrt{2}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-196)+140\sqrt{2}}{2*14}=\frac{196+140\sqrt{2}}{28}
$