X-8/9x=72

Solution for X-8/9x=72 equation:

X-8/9X=72

We move all terms to the left:

X-8/9X-(72)=0


Domain of the equation: 9X!=0

X!=0/9

X!=0

X∈R


We multiply all the terms by the denominator


X*9X-72*9X-8=0

Wy multiply elements

9X^2-648X-8=0

a = 9; b = -648; c = -8;
Δ = b2-4ac
Δ = -6482-4·9·(-8)
Δ = 420192
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:

$\sqrt{\Delta}=\sqrt{420192}=\sqrt{144*2918}=\sqrt{144}*\sqrt{2918}=12\sqrt{2918}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-648)-12\sqrt{2918}}{2*9}=\frac{648-12\sqrt{2918}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-648)+12\sqrt{2918}}{2*9}=\frac{648+12\sqrt{2918}}{18}
$