2/4x=-1/3x+5

Solution for 2/4x=-1/3x+5 equation:

2/4x=-1/3x+5

We move all terms to the left:

2/4x-(-1/3x+5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

2/4x+1/3x-5=0

We calculate fractions


6x/12x^2+4x/12x^2-5=0

We multiply all the terms by the denominator


6x+4x-5*12x^2=0

We add all the numbers together, and all the variables

10x-5*12x^2=0

Wy multiply elements

-60x^2+10x=0

a = -60; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-60)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-60}=\frac{-20}{-120}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-60}=\frac{0}{-120}
=0
$