1/2x+3/4=1/4x+6

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Solution for 1/2x+3/4=1/4x+6 equation:



1/2x+3/4=1/4x+6
We move all terms to the left:
1/2x+3/4-(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+3/4=0
We calculate fractions
64x/128x^2+(-2x)/128x^2+6x/128x^2-6=0
We multiply all the terms by the denominator
64x+(-2x)+6x-6*128x^2=0
We add all the numbers together, and all the variables
70x+(-2x)-6*128x^2=0
Wy multiply elements
-768x^2+70x+(-2x)=0
We get rid of parentheses
-768x^2+70x-2x=0
We add all the numbers together, and all the variables
-768x^2+68x=0
a = -768; b = 68; c = 0;
Δ = b2-4ac
Δ = 682-4·(-768)·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-68}{2*-768}=\frac{-136}{-1536} =17/192 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+68}{2*-768}=\frac{0}{-1536} =0 $

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