1/2x+4=3/42x-8

Solution for 1/2x+4=3/42x-8 equation:

1/2x+4=3/42x-8

We move all terms to the left:

1/2x+4-(3/42x-8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 42x-8)!=0

x∈R


We get rid of parentheses

1/2x-3/42x+8+4=0

We calculate fractions


42x/84x^2+(-6x)/84x^2+8+4=0

We add all the numbers together, and all the variables

42x/84x^2+(-6x)/84x^2+12=0

We multiply all the terms by the denominator


42x+(-6x)+12*84x^2=0

Wy multiply elements

1008x^2+42x+(-6x)=0

We get rid of parentheses

1008x^2+42x-6x=0

We add all the numbers together, and all the variables

1008x^2+36x=0

a = 1008; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·1008·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*1008}=\frac{-72}{2016}
=-1/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*1008}=\frac{0}{2016}
=0
$