x=5/9x-32

Solution for x=5/9x-32 equation:

x=5/9x-32

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

x-5/9x+32=0

We multiply all the terms by the denominator


x*9x+32*9x-5=0

Wy multiply elements

9x^2+288x-5=0

a = 9; b = 288; c = -5;
Δ = b2-4ac
Δ = 2882-4·9·(-5)
Δ = 83124
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:

$\sqrt{\Delta}=\sqrt{83124}=\sqrt{36*2309}=\sqrt{36}*\sqrt{2309}=6\sqrt{2309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-6\sqrt{2309}}{2*9}=\frac{-288-6\sqrt{2309}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+6\sqrt{2309}}{2*9}=\frac{-288+6\sqrt{2309}}{18}
$