3(x/2+16)-16=3/2x

Solution for 3(x/2+16)-16=3/2x equation:

3(x/2+16)-16=3/2x

We move all terms to the left:

3(x/2+16)-16-(3/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3(x/2+16)-(+3/2x)-16=0

We multiply parentheses

3x-(+3/2x)+48-16=0

We get rid of parentheses

3x-3/2x+48-16=0

We multiply all the terms by the denominator


3x*2x+48*2x-16*2x-3=0

Wy multiply elements

6x^2+96x-32x-3=0

We add all the numbers together, and all the variables

6x^2+64x-3=0

a = 6; b = 64; c = -3;
Δ = b2-4ac
Δ = 642-4·6·(-3)
Δ = 4168
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:

$\sqrt{\Delta}=\sqrt{4168}=\sqrt{4*1042}=\sqrt{4}*\sqrt{1042}=2\sqrt{1042}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-2\sqrt{1042}}{2*6}=\frac{-64-2\sqrt{1042}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+2\sqrt{1042}}{2*6}=\frac{-64+2\sqrt{1042}}{12}
$