1/8x+4=12-4x

Solution for 1/8x+4=12-4x equation:

1/8x+4=12-4x

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

32x^2-96x+32x+1=0

We add all the numbers together, and all the variables

32x^2-64x+1=0

a = 32; b = -64; c = +1;
Δ = b2-4ac
Δ = -642-4·32·1
Δ = 3968
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:

$\sqrt{\Delta}=\sqrt{3968}=\sqrt{64*62}=\sqrt{64}*\sqrt{62}=8\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{62}}{2*32}=\frac{64-8\sqrt{62}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{62}}{2*32}=\frac{64+8\sqrt{62}}{64}
$