5/2x+4/3x=2

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



5/2x+4/3x=2
We move all terms to the left:
5/2x+4/3x-(2)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We calculate fractions
15x/6x^2+8x/6x^2-2=0
We multiply all the terms by the denominator
15x+8x-2*6x^2=0
We add all the numbers together, and all the variables
23x-2*6x^2=0
Wy multiply elements
-12x^2+23x=0
a = -12; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-12)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-12}=\frac{-46}{-24} =1+11/12 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-12}=\frac{0}{-24} =0 $

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