5x/14x=12-x

Solution for 5x/14x=12-x equation:

5x/14x=12-x

We move all terms to the left:

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


Domain of the equation: 14x!=0

x!=0/14

x!=0

x∈R


We add all the numbers together, and all the variables

5x/14x-(-1x+12)=0

We get rid of parentheses

5x/14x+1x-12=0

We multiply all the terms by the denominator


5x+1x*14x-12*14x=0

Wy multiply elements

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

We add all the numbers together, and all the variables

14x^2-163x=0

a = 14; b = -163; c = 0;
Δ = b2-4ac
Δ = -1632-4·14·0
Δ = 26569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26569}=163$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-163)-163}{2*14}=\frac{0}{28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-163)+163}{2*14}=\frac{326}{28}
=11+9/14
$