1/2*x+4/3*x=33

Solution for 1/2*x+4/3*x=33 equation:

1/2x+4/3x=33

We move all terms to the left:

1/2x+4/3x-(33)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


3x/6x^2+8x/6x^2-33=0

We multiply all the terms by the denominator


3x+8x-33*6x^2=0

We add all the numbers together, and all the variables

11x-33*6x^2=0

Wy multiply elements

-198x^2+11x=0

a = -198; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-198)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-198}=\frac{-22}{-396}
=1/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-198}=\frac{0}{-396}
=0
$