75/x+x=120

Solution for 75/x+x=120 equation:

75/x+x=120

We move all terms to the left:

75/x+x-(120)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+75/x-120=0

We multiply all the terms by the denominator


x*x-120*x+75=0

We add all the numbers together, and all the variables

-120x+x*x+75=0

Wy multiply elements

x^2-120x+75=0

a = 1; b = -120; c = +75;
Δ = b2-4ac
Δ = -1202-4·1·75
Δ = 14100
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:

$\sqrt{\Delta}=\sqrt{14100}=\sqrt{100*141}=\sqrt{100}*\sqrt{141}=10\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-10\sqrt{141}}{2*1}=\frac{120-10\sqrt{141}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+10\sqrt{141}}{2*1}=\frac{120+10\sqrt{141}}{2}
$