4/8x+12=x

Solution for 4/8x+12=x equation:

4/8x+12=x

We move all terms to the left:

4/8x+12-(x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4/8x+12=0

We multiply all the terms by the denominator


-1x*8x+12*8x+4=0

Wy multiply elements

-8x^2+96x+4=0

a = -8; b = 96; c = +4;
Δ = b2-4ac
Δ = 962-4·(-8)·4
Δ = 9344
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:

$\sqrt{\Delta}=\sqrt{9344}=\sqrt{64*146}=\sqrt{64}*\sqrt{146}=8\sqrt{146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-8\sqrt{146}}{2*-8}=\frac{-96-8\sqrt{146}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+8\sqrt{146}}{2*-8}=\frac{-96+8\sqrt{146}}{-16}
$