180/x+x=28

Solution for 180/x+x=28 equation:

180/x+x=28

We move all terms to the left:

180/x+x-(28)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+180/x-28=0

We multiply all the terms by the denominator


x*x-28*x+180=0

We add all the numbers together, and all the variables

-28x+x*x+180=0

Wy multiply elements

x^2-28x+180=0

a = 1; b = -28; c = +180;
Δ = b2-4ac
Δ = -282-4·1·180
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-8}{2*1}=\frac{20}{2}
=10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+8}{2*1}=\frac{36}{2}
=18
$