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

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

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

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-12x^2+24x+16x+13=0

We add all the numbers together, and all the variables

-8x^2+40x+13=0

a = -8; b = 40; c = +13;
Δ = b2-4ac
Δ = 402-4·(-8)·13
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-12\sqrt{14}}{2*-8}=\frac{-40-12\sqrt{14}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+12\sqrt{14}}{2*-8}=\frac{-40+12\sqrt{14}}{-16}
$