X/12x-8-3x=10+5x-4

Solution for X/12x-8-3x=10+5x-4 equation:

X/12X-8-3X=10+5X-4

We move all terms to the left:

X/12X-8-3X-(10+5X-4)=0


Domain of the equation: 12X!=0

X!=0/12

X!=0

X∈R


We add all the numbers together, and all the variables

X/12X-3X-(5X+6)-8=0

We add all the numbers together, and all the variables

-3X+X/12X-(5X+6)-8=0

We get rid of parentheses

-3X+X/12X-5X-6-8=0

We multiply all the terms by the denominator


-3X*12X+X-5X*12X-6*12X-8*12X=0

We add all the numbers together, and all the variables

X-3X*12X-5X*12X-6*12X-8*12X=0

Wy multiply elements

-36X^2-60X^2+X-72X-96X=0

We add all the numbers together, and all the variables

-96X^2-167X=0

a = -96; b = -167; c = 0;
Δ = b2-4ac
Δ = -1672-4·(-96)·0
Δ = 27889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{27889}=167$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-167)-167}{2*-96}=\frac{0}{-192}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-167)+167}{2*-96}=\frac{334}{-192}
=-1+71/96
$