49-4/3x+x+4/3x=108

Solution for 49-4/3x+x+4/3x=108 equation:

49-4/3x+x+4/3x=108

We move all terms to the left:

49-4/3x+x+4/3x-(108)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x-4/3x+4/3x-59=0

We multiply all the terms by the denominator


x*3x-59*3x-4+4=0

We add all the numbers together, and all the variables

x*3x-59*3x=0

Wy multiply elements

3x^2-177x=0

a = 3; b = -177; c = 0;
Δ = b2-4ac
Δ = -1772-4·3·0
Δ = 31329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{31329}=177$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-177)-177}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-177)+177}{2*3}=\frac{354}{6}
=59
$