1/9*x=360

Solution for 1/9*x=360 equation:

1/9*x=360

We move all terms to the left:

1/9*x-(360)=0


Domain of the equation: 9*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-360*9*x+1=0

Wy multiply elements

-3240x*x+1=0

Wy multiply elements

-3240x^2+1=0

a = -3240; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-3240)·1
Δ = 12960
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:

$\sqrt{\Delta}=\sqrt{12960}=\sqrt{1296*10}=\sqrt{1296}*\sqrt{10}=36\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{10}}{2*-3240}=\frac{0-36\sqrt{10}}{-6480}
=-\frac{36\sqrt{10}}{-6480}
=-\frac{\sqrt{10}}{-180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{10}}{2*-3240}=\frac{0+36\sqrt{10}}{-6480}
=\frac{36\sqrt{10}}{-6480}
=\frac{\sqrt{10}}{-180}
$