2/8x+6-x=5x-12=

Solution for 2/8x+6-x=5x-12= equation:

2/8x+6-x=5x-12=

We move all terms to the left:

2/8x+6-x-(5x-12)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+2/8x-(5x-12)+6=0

We get rid of parentheses

-1x+2/8x-5x+12+6=0

We multiply all the terms by the denominator


-1x*8x-5x*8x+12*8x+6*8x+2=0

Wy multiply elements

-8x^2-40x^2+96x+48x+2=0

We add all the numbers together, and all the variables

-48x^2+144x+2=0

a = -48; b = 144; c = +2;
Δ = b2-4ac
Δ = 1442-4·(-48)·2
Δ = 21120
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:

$\sqrt{\Delta}=\sqrt{21120}=\sqrt{64*330}=\sqrt{64}*\sqrt{330}=8\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-8\sqrt{330}}{2*-48}=\frac{-144-8\sqrt{330}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+8\sqrt{330}}{2*-48}=\frac{-144+8\sqrt{330}}{-96}
$