6x^2-6x-12=-77/6

Solution for 6x^2-6x-12=-77/6 equation:

6x^2-6x-12=-77/6

We move all terms to the left:

6x^2-6x-12-(-77/6)=0

We get rid of parentheses

6x^2-6x-12+77/6=0

We multiply all the terms by the denominator


6x^2*6-6x*6+77-12*6=0

We add all the numbers together, and all the variables

6x^2*6-6x*6+5=0

Wy multiply elements

36x^2-36x+5=0

a = 36; b = -36; c = +5;
Δ = b2-4ac
Δ = -362-4·36·5
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-24}{2*36}=\frac{12}{72}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+24}{2*36}=\frac{60}{72}
=5/6
$