1/2x=2-3/4x

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



1/2x=2-3/4x
We move all terms to the left:
1/2x-(2-3/4x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
1/2x-(-3/4x+2)=0
We get rid of parentheses
1/2x+3/4x-2=0
We calculate fractions
4x/8x^2+6x/8x^2-2=0
We multiply all the terms by the denominator
4x+6x-2*8x^2=0
We add all the numbers together, and all the variables
10x-2*8x^2=0
Wy multiply elements
-16x^2+10x=0
a = -16; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-16)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-16}=\frac{-20}{-32} =5/8 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-16}=\frac{0}{-32} =0 $

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