0=12x^2-76x+55

Solution for 0=12x^2-76x+55 equation:

0=12x^2-76x+55

We move all terms to the left:

0-(12x^2-76x+55)=0

We add all the numbers together, and all the variables

-(12x^2-76x+55)=0

We get rid of parentheses

-12x^2+76x-55=0

a = -12; b = 76; c = -55;
Δ = b2-4ac
Δ = 762-4·(-12)·(-55)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-56}{2*-12}=\frac{-132}{-24}
=5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+56}{2*-12}=\frac{-20}{-24}
=5/6
$