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 = 636
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:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{159}}{2*3}=\frac{24-2\sqrt{159}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{159}}{2*3}=\frac{24+2\sqrt{159}}{6}
$