3/4x-5=1/2x+3

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Solution for 3/4x-5=1/2x+3 equation:



3/4x-5=1/2x+3
We move all terms to the left:
3/4x-5-(1/2x+3)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x+3)!=0
x∈R
We get rid of parentheses
3/4x-1/2x-3-5=0
We calculate fractions
6x/8x^2+(-4x)/8x^2-3-5=0
We add all the numbers together, and all the variables
6x/8x^2+(-4x)/8x^2-8=0
We multiply all the terms by the denominator
6x+(-4x)-8*8x^2=0
Wy multiply elements
-64x^2+6x+(-4x)=0
We get rid of parentheses
-64x^2+6x-4x=0
We add all the numbers together, and all the variables
-64x^2+2x=0
a = -64; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-64)·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*-64}=\frac{-4}{-128} =1/32 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-64}=\frac{0}{-128} =0 $

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