1/2x+8=6x-12-13/2x

Solution for 1/2x+8=6x-12-13/2x equation:

1/2x+8=6x-12-13/2x

We move all terms to the left:

1/2x+8-(6x-12-13/2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(6x-13/2x-12)+8=0

We get rid of parentheses

1/2x-6x+13/2x+12+8=0

We multiply all the terms by the denominator


-6x*2x+12*2x+8*2x+1+13=0

We add all the numbers together, and all the variables

-6x*2x+12*2x+8*2x+14=0

Wy multiply elements

-12x^2+24x+16x+14=0

We add all the numbers together, and all the variables

-12x^2+40x+14=0

a = -12; b = 40; c = +14;
Δ = b2-4ac
Δ = 402-4·(-12)·14
Δ = 2272
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:

$\sqrt{\Delta}=\sqrt{2272}=\sqrt{16*142}=\sqrt{16}*\sqrt{142}=4\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{142}}{2*-12}=\frac{-40-4\sqrt{142}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{142}}{2*-12}=\frac{-40+4\sqrt{142}}{-24}
$