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}
$