32/9x+2x=150

Solution for 32/9x+2x=150 equation:

32/9x+2x=150

We move all terms to the left:

32/9x+2x-(150)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

2x+32/9x-150=0

We multiply all the terms by the denominator


2x*9x-150*9x+32=0

Wy multiply elements

18x^2-1350x+32=0

a = 18; b = -1350; c = +32;
Δ = b2-4ac
Δ = -13502-4·18·32
Δ = 1820196
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:

$\sqrt{\Delta}=\sqrt{1820196}=\sqrt{36*50561}=\sqrt{36}*\sqrt{50561}=6\sqrt{50561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1350)-6\sqrt{50561}}{2*18}=\frac{1350-6\sqrt{50561}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1350)+6\sqrt{50561}}{2*18}=\frac{1350+6\sqrt{50561}}{36}
$