1/2x+3/5-4=20-1/3x

Solution for 1/2x+3/5-4=20-1/3x equation:

1/2x+3/5-4=20-1/3x

We move all terms to the left:

1/2x+3/5-4-(20-1/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-1/3x+20)-4+3/5=0

We get rid of parentheses

1/2x+1/3x-20-4+3/5=0

We calculate fractions


54x^2/150x^2+75x/150x^2+50x/150x^2-20-4=0

We add all the numbers together, and all the variables

54x^2/150x^2+75x/150x^2+50x/150x^2-24=0

We multiply all the terms by the denominator


54x^2+75x+50x-24*150x^2=0

We add all the numbers together, and all the variables

54x^2+125x-24*150x^2=0

Wy multiply elements

54x^2-3600x^2+125x=0

We add all the numbers together, and all the variables

-3546x^2+125x=0

a = -3546; b = 125; c = 0;
Δ = b2-4ac
Δ = 1252-4·(-3546)·0
Δ = 15625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15625}=125$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-125}{2*-3546}=\frac{-250}{-7092}
=125/3546
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+125}{2*-3546}=\frac{0}{-7092}
=0
$