2/4x+2/3x=7

Solution for 2/4x+2/3x=7 equation:

2/4x+2/3x=7

We move all terms to the left:

2/4x+2/3x-(7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


6x/12x^2+8x/12x^2-7=0

We multiply all the terms by the denominator


6x+8x-7*12x^2=0

We add all the numbers together, and all the variables

14x-7*12x^2=0

Wy multiply elements

-84x^2+14x=0

a = -84; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-84)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-84}=\frac{-28}{-168}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-84}=\frac{0}{-168}
=0
$