12000/x=7.2x

Solution for 12000/x=7.2x equation:

12000/x=7.2x

We move all terms to the left:

12000/x-(7.2x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

12000/x-(+7.2x)=0

We get rid of parentheses

12000/x-7.2x=0

We multiply all the terms by the denominator


-(7.2x)*x+12000=0

We add all the numbers together, and all the variables

-(+7.2x)*x+12000=0

We multiply parentheses

-7x^2+12000=0

a = -7; b = 0; c = +12000;
Δ = b2-4ac
Δ = 02-4·(-7)·12000
Δ = 336000
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:

$\sqrt{\Delta}=\sqrt{336000}=\sqrt{1600*210}=\sqrt{1600}*\sqrt{210}=40\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{210}}{2*-7}=\frac{0-40\sqrt{210}}{-14}
=-\frac{40\sqrt{210}}{-14}
=-\frac{20\sqrt{210}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{210}}{2*-7}=\frac{0+40\sqrt{210}}{-14}
=\frac{40\sqrt{210}}{-14}
=\frac{20\sqrt{210}}{-7}
$