8x+4/x=77

Solution for 8x+4/x=77 equation:

8x+4/x=77

We move all terms to the left:

8x+4/x-(77)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


8x*x-77*x+4=0

We add all the numbers together, and all the variables

-77x+8x*x+4=0

Wy multiply elements

8x^2-77x+4=0

a = 8; b = -77; c = +4;
Δ = b2-4ac
Δ = -772-4·8·4
Δ = 5801
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{-(-77)-\sqrt{5801}}{2*8}=\frac{77-\sqrt{5801}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+\sqrt{5801}}{2*8}=\frac{77+\sqrt{5801}}{16}
$