120+8x/12x=x

Solution for 120+8x/12x=x equation:

120+8x/12x=x

We move all terms to the left:

120+8x/12x-(x)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+8x/12x+120=0

We multiply all the terms by the denominator


-1x*12x+8x+120*12x=0

We add all the numbers together, and all the variables

8x-1x*12x+120*12x=0

Wy multiply elements

-12x^2+8x+1440x=0

We add all the numbers together, and all the variables

-12x^2+1448x=0

a = -12; b = 1448; c = 0;
Δ = b2-4ac
Δ = 14482-4·(-12)·0
Δ = 2096704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2096704}=1448$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1448)-1448}{2*-12}=\frac{-2896}{-24}
=120+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1448)+1448}{2*-12}=\frac{0}{-24}
=0
$