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

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

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

We move all terms to the left:

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

We get rid of parentheses

1/2x-6x+7-6=0

We multiply all the terms by the denominator


-6x*2x+7*2x-6*2x+1=0

Wy multiply elements

-12x^2+14x-12x+1=0

We add all the numbers together, and all the variables

-12x^2+2x+1=0

a = -12; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-12)·1
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{13}}{2*-12}=\frac{-2-2\sqrt{13}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{13}}{2*-12}=\frac{-2+2\sqrt{13}}{-24}
$