78/x+5x=391

Solution for 78/x+5x=391 equation:

78/x+5x=391

We move all terms to the left:

78/x+5x-(391)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x+78/x-391=0

We multiply all the terms by the denominator


5x*x-391*x+78=0

We add all the numbers together, and all the variables

-391x+5x*x+78=0

Wy multiply elements

5x^2-391x+78=0

a = 5; b = -391; c = +78;
Δ = b2-4ac
Δ = -3912-4·5·78
Δ = 151321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{151321}=389$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-391)-389}{2*5}=\frac{2}{10}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-391)+389}{2*5}=\frac{780}{10}
=78
$