(1/2)x+(1/3)x=12

Solution for (1/2)x+(1/3)x=12 equation:

(1/2)x+(1/3)x=12

We move all terms to the left:

(1/2)x+(1/3)x-(12)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)x+(+1/3)x-12=0

We multiply parentheses

x^2+x^2-12=0

We add all the numbers together, and all the variables

2x^2-12=0

a = 2; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·2·(-12)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*2}=\frac{0-4\sqrt{6}}{4}
=-\frac{4\sqrt{6}}{4}
=-\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*2}=\frac{0+4\sqrt{6}}{4}
=\frac{4\sqrt{6}}{4}
=\sqrt{6}
$