(x^2-x-6)/6=102

Solution for (x^2-x-6)/6=102 equation:

(x^2-x-6)/6=102

We move all terms to the left:

(x^2-x-6)/6-(102)=0

We multiply all the terms by the denominator


(x^2-x-6)-102*6=0

We add all the numbers together, and all the variables

(x^2-x-6)-612=0

We get rid of parentheses

x^2-x-6-612=0

We add all the numbers together, and all the variables

x^2-1x-618=0

a = 1; b = -1; c = -618;
Δ = b2-4ac
Δ = -12-4·1·(-618)
Δ = 2473
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{-(-1)-\sqrt{2473}}{2*1}=\frac{1-\sqrt{2473}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{2473}}{2*1}=\frac{1+\sqrt{2473}}{2}
$