7x-(900/x)=6200

Solution for 7x-(900/x)=6200 equation:

7x-(900/x)=6200

We move all terms to the left:

7x-(900/x)-(6200)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7x-(+900/x)-6200=0

We get rid of parentheses

7x-900/x-6200=0

We multiply all the terms by the denominator


7x*x-6200*x-900=0

We add all the numbers together, and all the variables

-6200x+7x*x-900=0

Wy multiply elements

7x^2-6200x-900=0

a = 7; b = -6200; c = -900;
Δ = b2-4ac
Δ = -62002-4·7·(-900)
Δ = 38465200
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:

$\sqrt{\Delta}=\sqrt{38465200}=\sqrt{400*96163}=\sqrt{400}*\sqrt{96163}=20\sqrt{96163}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6200)-20\sqrt{96163}}{2*7}=\frac{6200-20\sqrt{96163}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6200)+20\sqrt{96163}}{2*7}=\frac{6200+20\sqrt{96163}}{14}
$