X=1/9y-6

Solution for X=1/9y-6 equation:

X=1/9X-6

We move all terms to the left:

X-(1/9X-6)=0


Domain of the equation: 9X-6)!=0

X∈R


We get rid of parentheses

X-1/9X+6=0

We multiply all the terms by the denominator


X*9X+6*9X-1=0

Wy multiply elements

9X^2+54X-1=0

a = 9; b = 54; c = -1;
Δ = b2-4ac
Δ = 542-4·9·(-1)
Δ = 2952
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:

$\sqrt{\Delta}=\sqrt{2952}=\sqrt{36*82}=\sqrt{36}*\sqrt{82}=6\sqrt{82}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{82}}{2*9}=\frac{-54-6\sqrt{82}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{82}}{2*9}=\frac{-54+6\sqrt{82}}{18}
$