x=-5/3x-8

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

x=-5/3x-8

We move all terms to the left:

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


Domain of the equation: 3x-8)!=0

x∈R


We get rid of parentheses

x+5/3x+8=0

We multiply all the terms by the denominator


x*3x+8*3x+5=0

Wy multiply elements

3x^2+24x+5=0

a = 3; b = 24; c = +5;
Δ = b2-4ac
Δ = 242-4·3·5
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*3}=\frac{-24-2\sqrt{129}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{129}}{2*3}=\frac{-24+2\sqrt{129}}{6}
$