4/3x+6/4x=3

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
$