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

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



1/2x+6=3/4x-3
We move all terms to the left:
1/2x+6-(3/4x-3)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x-3)!=0
x∈R
We get rid of parentheses
1/2x-3/4x+3+6=0
We calculate fractions
4x/8x^2+(-6x)/8x^2+3+6=0
We add all the numbers together, and all the variables
4x/8x^2+(-6x)/8x^2+9=0
We multiply all the terms by the denominator
4x+(-6x)+9*8x^2=0
Wy multiply elements
72x^2+4x+(-6x)=0
We get rid of parentheses
72x^2+4x-6x=0
We add all the numbers together, and all the variables
72x^2-2x=0
a = 72; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·72·0
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*72}=\frac{0}{144} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*72}=\frac{4}{144} =1/36 $

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