(x)=8/3x-16

Solution for (x)=8/3x-16 equation:

(x)=8/3x-16

We move all terms to the left:

(x)-(8/3x-16)=0


Domain of the equation: 3x-16)!=0

x∈R


We get rid of parentheses

x-8/3x+16=0

We multiply all the terms by the denominator


x*3x+16*3x-8=0

Wy multiply elements

3x^2+48x-8=0

a = 3; b = 48; c = -8;
Δ = b2-4ac
Δ = 482-4·3·(-8)
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-20\sqrt{6}}{2*3}=\frac{-48-20\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+20\sqrt{6}}{2*3}=\frac{-48+20\sqrt{6}}{6}
$