3x=(5/9)(x-32)

Solution for 3x=(5/9)(x-32) equation:

3x=(5/9)(x-32)

We move all terms to the left:

3x-((5/9)(x-32))=0


Domain of the equation: 9)(x-32))!=0

x∈R


We add all the numbers together, and all the variables

3x-((+5/9)(x-32))=0

We multiply parentheses ..

-((+5x^2+5/9*-32))+3x=0

We multiply all the terms by the denominator


-((+5x^2+5+3x*9*-32))=0


We calculate terms in parentheses: -((+5x^2+5+3x*9*-32)), so:

(+5x^2+5+3x*9*-32)

We get rid of parentheses

5x^2+3x*9*+5-32

We add all the numbers together, and all the variables

5x^2+3x*9*-27

Wy multiply elements

5x^2+27x^2-27

We add all the numbers together, and all the variables

32x^2-27

Back to the equation:

-(32x^2-27)


We get rid of parentheses

-32x^2+27=0

a = -32; b = 0; c = +27;
Δ = b2-4ac
Δ = 02-4·(-32)·27
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{6}}{2*-32}=\frac{0-24\sqrt{6}}{-64}
=-\frac{24\sqrt{6}}{-64}
=-\frac{3\sqrt{6}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{6}}{2*-32}=\frac{0+24\sqrt{6}}{-64}
=\frac{24\sqrt{6}}{-64}
=\frac{3\sqrt{6}}{-8}
$