X=5/9u+9

Solution for X=5/9u+9 equation:

X=5/9X+9

We move all terms to the left:

X-(5/9X+9)=0


Domain of the equation: 9X+9)!=0

X∈R


We get rid of parentheses

X-5/9X-9=0

We multiply all the terms by the denominator


X*9X-9*9X-5=0

Wy multiply elements

9X^2-81X-5=0

a = 9; b = -81; c = -5;
Δ = b2-4ac
Δ = -812-4·9·(-5)
Δ = 6741
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:

$\sqrt{\Delta}=\sqrt{6741}=\sqrt{9*749}=\sqrt{9}*\sqrt{749}=3\sqrt{749}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-3\sqrt{749}}{2*9}=\frac{81-3\sqrt{749}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+3\sqrt{749}}{2*9}=\frac{81+3\sqrt{749}}{18}
$