-5x-1/3x=8

Solution for -5x-1/3x=8 equation:

-5x-1/3x=8

We move all terms to the left:

-5x-1/3x-(8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


-5x*3x-8*3x-1=0

Wy multiply elements

-15x^2-24x-1=0

a = -15; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·(-15)·(-1)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{129}}{2*-15}=\frac{24-2\sqrt{129}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{129}}{2*-15}=\frac{24+2\sqrt{129}}{-30}
$