21/4x+1/2x=33

Solution for 21/4x+1/2x=33 equation:

21/4x+1/2x=33

We move all terms to the left:

21/4x+1/2x-(33)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


42x/8x^2+4x/8x^2-33=0

We multiply all the terms by the denominator


42x+4x-33*8x^2=0

We add all the numbers together, and all the variables

46x-33*8x^2=0

Wy multiply elements

-264x^2+46x=0

a = -264; b = 46; c = 0;
Δ = b2-4ac
Δ = 462-4·(-264)·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-46}{2*-264}=\frac{-92}{-528}
=23/132
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+46}{2*-264}=\frac{0}{-528}
=0
$