5/4x+35x=48

Solution for 5/4x+35x=48 equation:

5/4x+35x=48

We move all terms to the left:

5/4x+35x-(48)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

35x+5/4x-48=0

We multiply all the terms by the denominator


35x*4x-48*4x+5=0

Wy multiply elements

140x^2-192x+5=0

a = 140; b = -192; c = +5;
Δ = b2-4ac
Δ = -1922-4·140·5
Δ = 34064
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:

$\sqrt{\Delta}=\sqrt{34064}=\sqrt{16*2129}=\sqrt{16}*\sqrt{2129}=4\sqrt{2129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-4\sqrt{2129}}{2*140}=\frac{192-4\sqrt{2129}}{280}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+4\sqrt{2129}}{2*140}=\frac{192+4\sqrt{2129}}{280}
$