10/3x=50,x=

Solution for 10/3x=50,x= equation:

10/3x=50.x=

We move all terms to the left:

10/3x-(50.x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

10/3x-(+50.x)=0

We get rid of parentheses

10/3x-50.x=0

We multiply all the terms by the denominator


-(50.x)*3x+10=0

We add all the numbers together, and all the variables

-(+50.x)*3x+10=0

We multiply parentheses

-150x^2+10=0

a = -150; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-150)·10
Δ = 6000
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:

$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{15}}{2*-150}=\frac{0-20\sqrt{15}}{-300}
=-\frac{20\sqrt{15}}{-300}
=-\frac{\sqrt{15}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{15}}{2*-150}=\frac{0+20\sqrt{15}}{-300}
=\frac{20\sqrt{15}}{-300}
=\frac{\sqrt{15}}{-15}
$