3/3x+3/4x=20

Solution for 3/3x+3/4x=20 equation:

3/3x+3/4x=20

We move all terms to the left:

3/3x+3/4x-(20)=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


12x/12x^2+9x/12x^2-20=0

We multiply all the terms by the denominator


12x+9x-20*12x^2=0

We add all the numbers together, and all the variables

21x-20*12x^2=0

Wy multiply elements

-240x^2+21x=0

a = -240; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-240)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-240}=\frac{-42}{-480}
=7/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-240}=\frac{0}{-480}
=0
$