-8/3x-4x+2/3x=-7

Solution for -8/3x-4x+2/3x=-7 equation:

-8/3x-4x+2/3x=-7

We move all terms to the left:

-8/3x-4x+2/3x-(-7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-4x-8/3x+2/3x+7=0

We multiply all the terms by the denominator


-4x*3x+7*3x-8+2=0

We add all the numbers together, and all the variables

-4x*3x+7*3x-6=0

Wy multiply elements

-12x^2+21x-6=0

a = -12; b = 21; c = -6;
Δ = b2-4ac
Δ = 212-4·(-12)·(-6)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{17}}{2*-12}=\frac{-21-3\sqrt{17}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{17}}{2*-12}=\frac{-21+3\sqrt{17}}{-24}
$