x=1/3(3x)-8

Solution for x=1/3(3x)-8 equation:

x=1/3(3x)-8

We move all terms to the left:

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


Domain of the equation: 33x-8)!=0

x∈R


We get rid of parentheses

x-1/33x+8=0

We multiply all the terms by the denominator


x*33x+8*33x-1=0

Wy multiply elements

33x^2+264x-1=0

a = 33; b = 264; c = -1;
Δ = b2-4ac
Δ = 2642-4·33·(-1)
Δ = 69828
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:

$\sqrt{\Delta}=\sqrt{69828}=\sqrt{2116*33}=\sqrt{2116}*\sqrt{33}=46\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(264)-46\sqrt{33}}{2*33}=\frac{-264-46\sqrt{33}}{66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(264)+46\sqrt{33}}{2*33}=\frac{-264+46\sqrt{33}}{66}
$