6(4/3x+3)=6(5/6x)

Solution for 6(4/3x+3)=6(5/6x) equation:

6(4/3x+3)=6(5/6x)

We move all terms to the left:

6(4/3x+3)-(6(5/6x))=0


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

x∈R



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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6(4/3x+3)-(6(+5/6x))=0

We multiply parentheses

24x-(6(+5/6x))+18=0

We multiply all the terms by the denominator


24x*6x))-(6(+18*6x))+5=0

Wy multiply elements

144x^2+108x=0

a = 144; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·144·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*144}=\frac{-216}{288}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*144}=\frac{0}{288}
=0
$