6/4x+3/8x=36/12

Solution for 6/4x+3/8x=36/12 equation:

6/4x+3/8x=36/12

We move all terms to the left:

6/4x+3/8x-(36/12)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

6/4x+3/8x-3=0

We calculate fractions


48x/32x^2+12x/32x^2-3=0

We multiply all the terms by the denominator


48x+12x-3*32x^2=0

We add all the numbers together, and all the variables

60x-3*32x^2=0

Wy multiply elements

-96x^2+60x=0

a = -96; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-96)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-96}=\frac{-120}{-192}
=5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-96}=\frac{0}{-192}
=0
$