1/2x^+3x=8

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

1/2x^+3x=8

We move all terms to the left:

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


Domain of the equation: 2x^!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-16x+1=0

a = 6; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·6·1
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{58}}{2*6}=\frac{16-2\sqrt{58}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{58}}{2*6}=\frac{16+2\sqrt{58}}{12}
$