x+5/6x=77

Solution for x+5/6x=77 equation:

x+5/6x=77

We move all terms to the left:

x+5/6x-(77)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


x*6x-77*6x+5=0

Wy multiply elements

6x^2-462x+5=0

a = 6; b = -462; c = +5;
Δ = b2-4ac
Δ = -4622-4·6·5
Δ = 213324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{213324}=\sqrt{4*53331}=\sqrt{4}*\sqrt{53331}=2\sqrt{53331}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-462)-2\sqrt{53331}}{2*6}=\frac{462-2\sqrt{53331}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-462)+2\sqrt{53331}}{2*6}=\frac{462+2\sqrt{53331}}{12}
$