x-4=(1/3)(6x-54)

Solution for x-4=(1/3)(6x-54) equation:

x-4=(1/3)(6x-54)

We move all terms to the left:

x-4-((1/3)(6x-54))=0


Domain of the equation: 3)(6x-54))!=0

x∈R


We add all the numbers together, and all the variables

x-((+1/3)(6x-54))-4=0

We multiply parentheses ..

-((+6x^2+1/3*-54))+x-4=0

We multiply all the terms by the denominator


-((+6x^2+1+x*3*-54))-4*3*-54))=0


We calculate terms in parentheses: -((+6x^2+1+x*3*-54)), so:

(+6x^2+1+x*3*-54)

We get rid of parentheses

6x^2+x*3*+1-54

We add all the numbers together, and all the variables

6x^2+x*3*-53

Wy multiply elements

6x^2+3x^2-53

We add all the numbers together, and all the variables

9x^2-53

Back to the equation:

-(9x^2-53)


We add all the numbers together, and all the variables

-(9x^2-53)=0

We get rid of parentheses

-9x^2+53=0

a = -9; b = 0; c = +53;
Δ = b2-4ac
Δ = 02-4·(-9)·53
Δ = 1908
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:

$\sqrt{\Delta}=\sqrt{1908}=\sqrt{36*53}=\sqrt{36}*\sqrt{53}=6\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{53}}{2*-9}=\frac{0-6\sqrt{53}}{-18}
=-\frac{6\sqrt{53}}{-18}
=-\frac{\sqrt{53}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{53}}{2*-9}=\frac{0+6\sqrt{53}}{-18}
=\frac{6\sqrt{53}}{-18}
=\frac{\sqrt{53}}{-3}
$