6x+(1/2)x=18

Solution for 6x+(1/2)x=18 equation:

6x+(1/2)x=18

We move all terms to the left:

6x+(1/2)x-(18)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x+(+1/2)x-18=0

We multiply parentheses

x^2+6x-18=0

a = 1; b = 6; c = -18;
Δ = b2-4ac
Δ = 62-4·1·(-18)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*1}=\frac{-6-6\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*1}=\frac{-6+6\sqrt{3}}{2}
$