1/2x+4/8x-4=3

Solution for 1/2x+4/8x-4=3 equation:

1/2x+4/8x-4=3

We move all terms to the left:

1/2x+4/8x-4-(3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+4/8x-7=0

We calculate fractions


8x/16x^2+8x/16x^2-7=0

We multiply all the terms by the denominator


8x+8x-7*16x^2=0

We add all the numbers together, and all the variables

16x-7*16x^2=0

Wy multiply elements

-112x^2+16x=0

a = -112; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-112)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-112}=\frac{-32}{-224}
=1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-112}=\frac{0}{-224}
=0
$