3x=(1/2)(x+8+32)

Solution for 3x=(1/2)(x+8+32) equation:

3x=(1/2)(x+8+32)

We move all terms to the left:

3x-((1/2)(x+8+32))=0


Domain of the equation: 2)(x+8+32))!=0

We move all terms containing x to the left, all other terms to the right

2)(x+32))!=-8

x∈R


We add all the numbers together, and all the variables

3x-((+1/2)(x+40))=0

We multiply parentheses ..

-((+x^2+1/2*40))+3x=0

We multiply all the terms by the denominator


-((+x^2+1+3x*2*40))=0


We calculate terms in parentheses: -((+x^2+1+3x*2*40)), so:

(+x^2+1+3x*2*40)

We get rid of parentheses

x^2+3x*2*40+1

Wy multiply elements

x^2+240x*4+1

Wy multiply elements

x^2+960x+1

Back to the equation:

-(x^2+960x+1)


We get rid of parentheses

-x^2-960x-1=0

We add all the numbers together, and all the variables

-1x^2-960x-1=0

a = -1; b = -960; c = -1;
Δ = b2-4ac
Δ = -9602-4·(-1)·(-1)
Δ = 921596
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:

$\sqrt{\Delta}=\sqrt{921596}=\sqrt{4*230399}=\sqrt{4}*\sqrt{230399}=2\sqrt{230399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-960)-2\sqrt{230399}}{2*-1}=\frac{960-2\sqrt{230399}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-960)+2\sqrt{230399}}{2*-1}=\frac{960+2\sqrt{230399}}{-2}
$