1/2x+8=1/4x-6

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Solution for 1/2x+8=1/4x-6 equation:



1/2x+8=1/4x-6
We move all terms to the left:
1/2x+8-(1/4x-6)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x-6)!=0
x∈R
We get rid of parentheses
1/2x-1/4x+6+8=0
We calculate fractions
4x/8x^2+(-2x)/8x^2+6+8=0
We add all the numbers together, and all the variables
4x/8x^2+(-2x)/8x^2+14=0
We multiply all the terms by the denominator
4x+(-2x)+14*8x^2=0
Wy multiply elements
112x^2+4x+(-2x)=0
We get rid of parentheses
112x^2+4x-2x=0
We add all the numbers together, and all the variables
112x^2+2x=0
a = 112; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·112·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*112}=\frac{-4}{224} =-1/56 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*112}=\frac{0}{224} =0 $

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