1/3x=60;x=

Solution for 1/3x=60;x= equation:

1/3x=60x=

We move all terms to the left:

1/3x-(60x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-60x+1/3x=0

We multiply all the terms by the denominator


-60x*3x+1=0

Wy multiply elements

-180x^2+1=0

a = -180; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-180)·1
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*-180}=\frac{0-12\sqrt{5}}{-360}
=-\frac{12\sqrt{5}}{-360}
=-\frac{\sqrt{5}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*-180}=\frac{0+12\sqrt{5}}{-360}
=\frac{12\sqrt{5}}{-360}
=\frac{\sqrt{5}}{-30}
$