(1/3)(6x-12)+5x=17

Solution for (1/3)(6x-12)+5x=17 equation:

(1/3)(6x-12)+5x=17

We move all terms to the left:

(1/3)(6x-12)+5x-(17)=0


Domain of the equation: 3)(6x-12)!=0

x∈R


We add all the numbers together, and all the variables

(+1/3)(6x-12)+5x-17=0

We add all the numbers together, and all the variables

5x+(+1/3)(6x-12)-17=0

We multiply parentheses ..

(+6x^2+1/3*-12)+5x-17=0

We multiply all the terms by the denominator


(+6x^2+1+5x*3*-12)-17*3*-12)=0

We add all the numbers together, and all the variables

(+6x^2+1+5x*3*-12)=0

We get rid of parentheses

6x^2+5x*3*+1-12=0

We add all the numbers together, and all the variables

6x^2+5x*3*-11=0

Wy multiply elements

6x^2+15x^2-11=0

We add all the numbers together, and all the variables

21x^2-11=0

a = 21; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·21·(-11)
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{231}}{2*21}=\frac{0-2\sqrt{231}}{42}
=-\frac{2\sqrt{231}}{42}
=-\frac{\sqrt{231}}{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{231}}{2*21}=\frac{0+2\sqrt{231}}{42}
=\frac{2\sqrt{231}}{42}
=\frac{\sqrt{231}}{21}
$