150x=10000/(7x)

Solution for 150x=10000/(7x) equation:

150x=10000/(7x)

We move all terms to the left:

150x-(10000/(7x))=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

150x-(+10000/7x)=0

We get rid of parentheses

150x-10000/7x=0

We multiply all the terms by the denominator


150x*7x-10000=0

Wy multiply elements

1050x^2-10000=0

a = 1050; b = 0; c = -10000;
Δ = b2-4ac
Δ = 02-4·1050·(-10000)
Δ = 42000000
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:

$\sqrt{\Delta}=\sqrt{42000000}=\sqrt{1000000*42}=\sqrt{1000000}*\sqrt{42}=1000\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1000\sqrt{42}}{2*1050}=\frac{0-1000\sqrt{42}}{2100}
=-\frac{1000\sqrt{42}}{2100}
=-\frac{10\sqrt{42}}{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1000\sqrt{42}}{2*1050}=\frac{0+1000\sqrt{42}}{2100}
=\frac{1000\sqrt{42}}{2100}
=\frac{10\sqrt{42}}{21}
$