6x(1/2x)+3x=8

Solution for 6x(1/2x)+3x=8 equation:

6x(1/2x)+3x=8

We move all terms to the left:

6x(1/2x)+3x-(8)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x(+1/2x)+3x-8=0

We add all the numbers together, and all the variables

3x+6x(+1/2x)-8=0

We multiply parentheses

6x^2+3x-8=0

a = 6; b = 3; c = -8;
Δ = b2-4ac
Δ = 32-4·6·(-8)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{201}}{2*6}=\frac{-3-\sqrt{201}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{201}}{2*6}=\frac{-3+\sqrt{201}}{12}
$