x=(5/9)(2x-32)

Solution for x=(5/9)(2x-32) equation:

x=(5/9)(2x-32)

We move all terms to the left:

x-((5/9)(2x-32))=0


Domain of the equation: 9)(2x-32))!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+10x^2+5/9*-32))+x=0

We multiply all the terms by the denominator


-((+10x^2+5+x*9*-32))=0


We calculate terms in parentheses: -((+10x^2+5+x*9*-32)), so:

(+10x^2+5+x*9*-32)

We get rid of parentheses

10x^2+x*9*+5-32

We add all the numbers together, and all the variables

10x^2+x*9*-27

Wy multiply elements

10x^2+9x^2-27

We add all the numbers together, and all the variables

19x^2-27

Back to the equation:

-(19x^2-27)


We get rid of parentheses

-19x^2+27=0

a = -19; b = 0; c = +27;
Δ = b2-4ac
Δ = 02-4·(-19)·27
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{57}}{2*-19}=\frac{0-6\sqrt{57}}{-38}
=-\frac{6\sqrt{57}}{-38}
=-\frac{3\sqrt{57}}{-19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{57}}{2*-19}=\frac{0+6\sqrt{57}}{-38}
=\frac{6\sqrt{57}}{-38}
=\frac{3\sqrt{57}}{-19}
$