1/9x=x-16

Solution for 1/9x=x-16 equation:

1/9x=x-16

We move all terms to the left:

1/9x-(x-16)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

1/9x-x+16=0

We multiply all the terms by the denominator


-x*9x+16*9x+1=0

Wy multiply elements

-9x^2+144x+1=0

a = -9; b = 144; c = +1;
Δ = b2-4ac
Δ = 1442-4·(-9)·1
Δ = 20772
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:

$\sqrt{\Delta}=\sqrt{20772}=\sqrt{36*577}=\sqrt{36}*\sqrt{577}=6\sqrt{577}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-6\sqrt{577}}{2*-9}=\frac{-144-6\sqrt{577}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+6\sqrt{577}}{2*-9}=\frac{-144+6\sqrt{577}}{-18}
$