5/4x+x=120

Solution for 5/4x+x=120 equation:

5/4x+x=120

We move all terms to the left:

5/4x+x-(120)=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-120=0

We multiply all the terms by the denominator


x*4x-120*4x+5=0

Wy multiply elements

4x^2-480x+5=0

a = 4; b = -480; c = +5;
Δ = b2-4ac
Δ = -4802-4·4·5
Δ = 230320
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:

$\sqrt{\Delta}=\sqrt{230320}=\sqrt{16*14395}=\sqrt{16}*\sqrt{14395}=4\sqrt{14395}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-4\sqrt{14395}}{2*4}=\frac{480-4\sqrt{14395}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+4\sqrt{14395}}{2*4}=\frac{480+4\sqrt{14395}}{8}
$