-4/3x-1/2=21/6x-4

Solution for -4/3x-1/2=21/6x-4 equation:

-4/3x-1/2=21/6x-4

We move all terms to the left:

-4/3x-1/2-(21/6x-4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x-4)!=0

x∈R


We get rid of parentheses

-4/3x-21/6x+4-1/2=0

We calculate fractions


(-108x^2)/72x^2+(-96x)/72x^2+(-252x)/72x^2+4=0

We multiply all the terms by the denominator


(-108x^2)+(-96x)+(-252x)+4*72x^2=0

Wy multiply elements

(-108x^2)+288x^2+(-96x)+(-252x)=0

We get rid of parentheses

-108x^2+288x^2-96x-252x=0

We add all the numbers together, and all the variables

180x^2-348x=0

a = 180; b = -348; c = 0;
Δ = b2-4ac
Δ = -3482-4·180·0
Δ = 121104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121104}=348$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-348)-348}{2*180}=\frac{0}{360}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-348)+348}{2*180}=\frac{696}{360}
=1+14/15
$