x+5/4x+3/4x=2400

Solution for x+5/4x+3/4x=2400 equation:

x+5/4x+3/4x=2400

We move all terms to the left:

x+5/4x+3/4x-(2400)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-2400*4x+5+3=0

We add all the numbers together, and all the variables

x*4x-2400*4x+8=0

Wy multiply elements

4x^2-9600x+8=0

a = 4; b = -9600; c = +8;
Δ = b2-4ac
Δ = -96002-4·4·8
Δ = 92159872
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:

$\sqrt{\Delta}=\sqrt{92159872}=\sqrt{64*1439998}=\sqrt{64}*\sqrt{1439998}=8\sqrt{1439998}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9600)-8\sqrt{1439998}}{2*4}=\frac{9600-8\sqrt{1439998}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9600)+8\sqrt{1439998}}{2*4}=\frac{9600+8\sqrt{1439998}}{8}
$