1/2x+4=1/8x+88

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Solution for 1/2x+4=1/8x+88 equation:



1/2x+4=1/8x+88
We move all terms to the left:
1/2x+4-(1/8x+88)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 8x+88)!=0
x∈R
We get rid of parentheses
1/2x-1/8x-88+4=0
We calculate fractions
8x/16x^2+(-2x)/16x^2-88+4=0
We add all the numbers together, and all the variables
8x/16x^2+(-2x)/16x^2-84=0
We multiply all the terms by the denominator
8x+(-2x)-84*16x^2=0
Wy multiply elements
-1344x^2+8x+(-2x)=0
We get rid of parentheses
-1344x^2+8x-2x=0
We add all the numbers together, and all the variables
-1344x^2+6x=0
a = -1344; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-1344)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-1344}=\frac{-12}{-2688} =1/224 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-1344}=\frac{0}{-2688} =0 $

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