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

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

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

We move all terms to the left:

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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -12; b = 40; c = +12;
Δ = b2-4ac
Δ = 402-4·(-12)·12
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{34}}{2*-12}=\frac{-40-8\sqrt{34}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{34}}{2*-12}=\frac{-40+8\sqrt{34}}{-24}
$