5/2x+7/4=2+5/6x

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Solution for 5/2x+7/4=2+5/6x equation:



5/2x+7/4=2+5/6x
We move all terms to the left:
5/2x+7/4-(2+5/6x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 6x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
5/2x-(5/6x+2)+7/4=0
We get rid of parentheses
5/2x-5/6x-2+7/4=0
We calculate fractions
504x^2/192x^2+480x/192x^2+(-160x)/192x^2-2=0
We multiply all the terms by the denominator
504x^2+480x+(-160x)-2*192x^2=0
Wy multiply elements
504x^2-384x^2+480x+(-160x)=0
We get rid of parentheses
504x^2-384x^2+480x-160x=0
We add all the numbers together, and all the variables
120x^2+320x=0
a = 120; b = 320; c = 0;
Δ = b2-4ac
Δ = 3202-4·120·0
Δ = 102400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{102400}=320$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-320}{2*120}=\frac{-640}{240} =-2+2/3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+320}{2*120}=\frac{0}{240} =0 $

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