1/2x+3x-7=6+6

Solution for 1/2x+3x-7=6+6 equation:

1/2x+3x-7=6+6

We move all terms to the left:

1/2x+3x-7-(6+6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+3x-7-12=0

We add all the numbers together, and all the variables

3x+1/2x-19=0

We multiply all the terms by the denominator


3x*2x-19*2x+1=0

Wy multiply elements

6x^2-38x+1=0

a = 6; b = -38; c = +1;
Δ = b2-4ac
Δ = -382-4·6·1
Δ = 1420
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:

$\sqrt{\Delta}=\sqrt{1420}=\sqrt{4*355}=\sqrt{4}*\sqrt{355}=2\sqrt{355}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{355}}{2*6}=\frac{38-2\sqrt{355}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{355}}{2*6}=\frac{38+2\sqrt{355}}{12}
$