5/4x+x=48

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

5/4x+x=48

We move all terms to the left:

5/4x+x-(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

x+5/4x-48=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-192x+5=0

a = 4; b = -192; c = +5;
Δ = b2-4ac
Δ = -1922-4·4·5
Δ = 36784
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:

$\sqrt{\Delta}=\sqrt{36784}=\sqrt{1936*19}=\sqrt{1936}*\sqrt{19}=44\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-44\sqrt{19}}{2*4}=\frac{192-44\sqrt{19}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+44\sqrt{19}}{2*4}=\frac{192+44\sqrt{19}}{8}
$