32/3*x=44

Solution for 32/3*x=44 equation:

32/3*x=44

We move all terms to the left:

32/3*x-(44)=0


Domain of the equation: 3*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-44*3*x+32=0

Wy multiply elements

-132x*x+32=0

Wy multiply elements

-132x^2+32=0

a = -132; b = 0; c = +32;
Δ = b2-4ac
Δ = 02-4·(-132)·32
Δ = 16896
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:

$\sqrt{\Delta}=\sqrt{16896}=\sqrt{256*66}=\sqrt{256}*\sqrt{66}=16\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{66}}{2*-132}=\frac{0-16\sqrt{66}}{-264}
=-\frac{16\sqrt{66}}{-264}
=-\frac{2\sqrt{66}}{-33}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{66}}{2*-132}=\frac{0+16\sqrt{66}}{-264}
=\frac{16\sqrt{66}}{-264}
=\frac{2\sqrt{66}}{-33}
$