x+8/3x=77

Solution for x+8/3x=77 equation:

x+8/3x=77

We move all terms to the left:

x+8/3x-(77)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-77*3x+8=0

Wy multiply elements

3x^2-231x+8=0

a = 3; b = -231; c = +8;
Δ = b2-4ac
Δ = -2312-4·3·8
Δ = 53265
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{-(-231)-\sqrt{53265}}{2*3}=\frac{231-\sqrt{53265}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-231)+\sqrt{53265}}{2*3}=\frac{231+\sqrt{53265}}{6}
$