x+4/3x+5.50=26.50

Solution for x+4/3x+5.50=26.50 equation:

x+4/3x+5.50=26.50

We move all terms to the left:

x+4/3x+5.50-(26.50)=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+5.50-(26.5)=0

We add all the numbers together, and all the variables

x+4/3x-21=0

We multiply all the terms by the denominator


x*3x-21*3x+4=0

Wy multiply elements

3x^2-63x+4=0

a = 3; b = -63; c = +4;
Δ = b2-4ac
Δ = -632-4·3·4
Δ = 3921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-\sqrt{3921}}{2*3}=\frac{63-\sqrt{3921}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{3921}}{2*3}=\frac{63+\sqrt{3921}}{6}
$