1/3x+3(x-2)=10

Solution for 1/3x+3(x-2)=10 equation:

1/3x+3(x-2)=10

We move all terms to the left:

1/3x+3(x-2)-(10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply parentheses

1/3x+3x-6-10=0

We multiply all the terms by the denominator


3x*3x-6*3x-10*3x+1=0

Wy multiply elements

9x^2-18x-30x+1=0

We add all the numbers together, and all the variables

9x^2-48x+1=0

a = 9; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·9·1
Δ = 2268
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:

$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-18\sqrt{7}}{2*9}=\frac{48-18\sqrt{7}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+18\sqrt{7}}{2*9}=\frac{48+18\sqrt{7}}{18}
$