1/4x+2/6x=20

Solution for 1/4x+2/6x=20 equation:

1/4x+2/6x=20

We move all terms to the left:

1/4x+2/6x-(20)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


6x/24x^2+8x/24x^2-20=0

We multiply all the terms by the denominator


6x+8x-20*24x^2=0

We add all the numbers together, and all the variables

14x-20*24x^2=0

Wy multiply elements

-480x^2+14x=0

a = -480; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-480)·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*-480}=\frac{-28}{-960}
=7/240
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-480}=\frac{0}{-960}
=0
$