7x-(2100+7/2x)=0

Solution for 7x-(2100+7/2x)=0 equation:

7x-(2100+7/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7x-(7/2x+2100)=0

We get rid of parentheses

7x-7/2x-2100=0

We multiply all the terms by the denominator


7x*2x-2100*2x-7=0

Wy multiply elements

14x^2-4200x-7=0

a = 14; b = -4200; c = -7;
Δ = b2-4ac
Δ = -42002-4·14·(-7)
Δ = 17640392
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:

$\sqrt{\Delta}=\sqrt{17640392}=\sqrt{196*90002}=\sqrt{196}*\sqrt{90002}=14\sqrt{90002}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4200)-14\sqrt{90002}}{2*14}=\frac{4200-14\sqrt{90002}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4200)+14\sqrt{90002}}{2*14}=\frac{4200+14\sqrt{90002}}{28}
$