4/5x+x=120

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

4/5x+x=120

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x+4/5x-120=0

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2-600x+4=0

a = 5; b = -600; c = +4;
Δ = b2-4ac
Δ = -6002-4·5·4
Δ = 359920
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:

$\sqrt{\Delta}=\sqrt{359920}=\sqrt{16*22495}=\sqrt{16}*\sqrt{22495}=4\sqrt{22495}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-4\sqrt{22495}}{2*5}=\frac{600-4\sqrt{22495}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+4\sqrt{22495}}{2*5}=\frac{600+4\sqrt{22495}}{10}
$