X=77-5/6x

Solution for X=77-5/6x equation:

X=77-5/6X

We move all terms to the left:

X-(77-5/6X)=0


Domain of the equation: 6X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

X+5/6X-77=0

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}
$