(X-4)(80/x+1)=80

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Solution for (X-4)(80/x+1)=80 equation: 



(X-4)(80/X+1)=80

We move all terms to the left:

(X-4)(80/X+1)-(80)=0



Domain of the equation: X+1)!=0

X∈R



We multiply parentheses ..

(+80X^2+X-320X-4)-80=0

We get rid of parentheses

80X^2+X-320X-4-80=0

We add all the numbers together, and all the variables

80X^2-319X-84=0

a = 80; b = -319; c = -84;
Δ = b2-4ac
Δ = -3192-4·80·(-84)
Δ = 128641
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{-(-319)-\sqrt{128641}}{2*80}=\frac{319-\sqrt{128641}}{160}
$


$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-319)+\sqrt{128641}}{2*80}=\frac{319+\sqrt{128641}}{160}
$

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