3x+4=8-1/2x

Solution for 3x+4=8-1/2x equation:

3x+4=8-1/2x

We move all terms to the left:

3x+4-(8-1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(-1/2x+8)+4=0

We get rid of parentheses

3x+1/2x-8+4=0

We multiply all the terms by the denominator


3x*2x-8*2x+4*2x+1=0

Wy multiply elements

6x^2-16x+8x+1=0

We add all the numbers together, and all the variables

6x^2-8x+1=0

a = 6; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·6·1
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{10}}{2*6}=\frac{8-2\sqrt{10}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{10}}{2*6}=\frac{8+2\sqrt{10}}{12}
$