X+6(-8-2/3)x=18

Solution for X+6(-8-2/3)x=18 equation:

X+6(-8-2/3)X=18

We move all terms to the left:

X+6(-8-2/3)X-(18)=0


Domain of the equation: 3)X!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+6(-2/3-8)X-18=0

We multiply parentheses

-12X^2+X-48X-18=0

We add all the numbers together, and all the variables

-12X^2-47X-18=0

a = -12; b = -47; c = -18;
Δ = b2-4ac
Δ = -472-4·(-12)·(-18)
Δ = 1345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-\sqrt{1345}}{2*-12}=\frac{47-\sqrt{1345}}{-24}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{1345}}{2*-12}=\frac{47+\sqrt{1345}}{-24}
$