1/9x+x=180

Solution for 1/9x+x=180 equation:

1/9x+x=180

We move all terms to the left:

1/9x+x-(180)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/9x-180=0

We multiply all the terms by the denominator


x*9x-180*9x+1=0

Wy multiply elements

9x^2-1620x+1=0

a = 9; b = -1620; c = +1;
Δ = b2-4ac
Δ = -16202-4·9·1
Δ = 2624364
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:

$\sqrt{\Delta}=\sqrt{2624364}=\sqrt{36*72899}=\sqrt{36}*\sqrt{72899}=6\sqrt{72899}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1620)-6\sqrt{72899}}{2*9}=\frac{1620-6\sqrt{72899}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1620)+6\sqrt{72899}}{2*9}=\frac{1620+6\sqrt{72899}}{18}
$