(-1/3*x)+1=-7

Solution for (-1/3*x)+1=-7 equation:

(-1/3*x)+1=-7

We move all terms to the left:

(-1/3*x)+1-(-7)=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

(-1/3*x)+8=0

We get rid of parentheses

-1/3*x+8=0

We multiply all the terms by the denominator


8*3*x-1=0

Wy multiply elements

24x*x-1=0

Wy multiply elements

24x^2-1=0

a = 24; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·24·(-1)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*24}=\frac{0-4\sqrt{6}}{48}
=-\frac{4\sqrt{6}}{48}
=-\frac{\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*24}=\frac{0+4\sqrt{6}}{48}
=\frac{4\sqrt{6}}{48}
=\frac{\sqrt{6}}{12}
$