300/4x=20+8x

Solution for 300/4x=20+8x equation:

300/4x=20+8x

We move all terms to the left:

300/4x-(20+8x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

300/4x-(8x+20)=0

We get rid of parentheses

300/4x-8x-20=0

We multiply all the terms by the denominator


-8x*4x-20*4x+300=0

Wy multiply elements

-32x^2-80x+300=0

a = -32; b = -80; c = +300;
Δ = b2-4ac
Δ = -802-4·(-32)·300
Δ = 44800
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:

$\sqrt{\Delta}=\sqrt{44800}=\sqrt{6400*7}=\sqrt{6400}*\sqrt{7}=80\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-80\sqrt{7}}{2*-32}=\frac{80-80\sqrt{7}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+80\sqrt{7}}{2*-32}=\frac{80+80\sqrt{7}}{-64}
$