(x+12)+x=5/14x+x

Solution for (x+12)+x=5/14x+x equation:

(x+12)+x=5/14x+x

We move all terms to the left:

(x+12)+x-(5/14x+x)=0


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

x∈R


We add all the numbers together, and all the variables

(x+12)+x-(+x+5/14x)=0

We add all the numbers together, and all the variables

x+(x+12)-(+x+5/14x)=0

We get rid of parentheses

x+x-x-5/14x+12=0

We multiply all the terms by the denominator


x*14x+x*14x-x*14x+12*14x-5=0

Wy multiply elements

14x^2+14x^2-14x^2+168x-5=0

We add all the numbers together, and all the variables

14x^2+168x-5=0

a = 14; b = 168; c = -5;
Δ = b2-4ac
Δ = 1682-4·14·(-5)
Δ = 28504
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:

$\sqrt{\Delta}=\sqrt{28504}=\sqrt{4*7126}=\sqrt{4}*\sqrt{7126}=2\sqrt{7126}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-2\sqrt{7126}}{2*14}=\frac{-168-2\sqrt{7126}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+2\sqrt{7126}}{2*14}=\frac{-168+2\sqrt{7126}}{28}
$