49-2/3x=32-6x

Solution for 49-2/3x=32-6x equation:

49-2/3x=32-6x

We move all terms to the left:

49-2/3x-(32-6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-2/3x-(-6x+32)+49=0

We get rid of parentheses

-2/3x+6x-32+49=0

We multiply all the terms by the denominator


6x*3x-32*3x+49*3x-2=0

Wy multiply elements

18x^2-96x+147x-2=0

We add all the numbers together, and all the variables

18x^2+51x-2=0

a = 18; b = 51; c = -2;
Δ = b2-4ac
Δ = 512-4·18·(-2)
Δ = 2745
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2745}=\sqrt{9*305}=\sqrt{9}*\sqrt{305}=3\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-3\sqrt{305}}{2*18}=\frac{-51-3\sqrt{305}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+3\sqrt{305}}{2*18}=\frac{-51+3\sqrt{305}}{36}
$