4x-400=10/3x

Solution for 4x-400=10/3x equation:

4x-400=10/3x

We move all terms to the left:

4x-400-(10/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+10/3x)-400=0

We get rid of parentheses

4x-10/3x-400=0

We multiply all the terms by the denominator


4x*3x-400*3x-10=0

Wy multiply elements

12x^2-1200x-10=0

a = 12; b = -1200; c = -10;
Δ = b2-4ac
Δ = -12002-4·12·(-10)
Δ = 1440480
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:

$\sqrt{\Delta}=\sqrt{1440480}=\sqrt{16*90030}=\sqrt{16}*\sqrt{90030}=4\sqrt{90030}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-4\sqrt{90030}}{2*12}=\frac{1200-4\sqrt{90030}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+4\sqrt{90030}}{2*12}=\frac{1200+4\sqrt{90030}}{24}
$