4/3x+6/4x=3

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Solution for 4/3x+6/4x=3 equation:



4/3x+6/4x=3
We move all terms to the left:
4/3x+6/4x-(3)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We calculate fractions
16x/12x^2+18x/12x^2-3=0
We multiply all the terms by the denominator
16x+18x-3*12x^2=0
We add all the numbers together, and all the variables
34x-3*12x^2=0
Wy multiply elements
-36x^2+34x=0
a = -36; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-36)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-36}=\frac{-68}{-72} =17/18 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-36}=\frac{0}{-72} =0 $

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