3(x/2-16)-30=50-1/3x

Solution for 3(x/2-16)-30=50-1/3x equation:

3(x/2-16)-30=50-1/3x

We move all terms to the left:

3(x/2-16)-30-(50-1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3(x/2-16)-(-1/3x+50)-30=0

We multiply parentheses

3x-(-1/3x+50)-48-30=0

We get rid of parentheses

3x+1/3x-50-48-30=0

We multiply all the terms by the denominator


3x*3x-50*3x-48*3x-30*3x+1=0

Wy multiply elements

9x^2-150x-144x-90x+1=0

We add all the numbers together, and all the variables

9x^2-384x+1=0

a = 9; b = -384; c = +1;
Δ = b2-4ac
Δ = -3842-4·9·1
Δ = 147420
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:

$\sqrt{\Delta}=\sqrt{147420}=\sqrt{324*455}=\sqrt{324}*\sqrt{455}=18\sqrt{455}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-384)-18\sqrt{455}}{2*9}=\frac{384-18\sqrt{455}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-384)+18\sqrt{455}}{2*9}=\frac{384+18\sqrt{455}}{18}
$