(x-8)(120/x+0.50)=120

Solution for (x-8)(120/x+0.50)=120 equation:

(x-8)(120/x+0.50)=120

We move all terms to the left:

(x-8)(120/x+0.50)-(120)=0


Domain of the equation: x+0.50)!=0

x∈R


We add all the numbers together, and all the variables

(x-8)(120/x+0.5)-120=0

We multiply parentheses ..

(+120x^2+0.5x-960x-4)-120=0

We get rid of parentheses

120x^2+0.5x-960x-4-120=0

We add all the numbers together, and all the variables

120x^2-959.5x-124=0

a = 120; b = -959.5; c = -124;
Δ = b2-4ac
Δ = -959.52-4·120·(-124)
Δ = 980160.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-959.5)-\sqrt{980160.25}}{2*120}=\frac{959.5-\sqrt{980160.25}}{240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-959.5)+\sqrt{980160.25}}{2*120}=\frac{959.5+\sqrt{980160.25}}{240}
$