55=3x2-12x+40

Solution for 55=3x2-12x+40 equation:

55=3x^2-12x+40

We move all terms to the left:

55-(3x^2-12x+40)=0

We get rid of parentheses

-3x^2+12x-40+55=0

We add all the numbers together, and all the variables

-3x^2+12x+15=0

a = -3; b = 12; c = +15;
Δ = b2-4ac
Δ = 122-4·(-3)·15
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-18}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+18}{2*-3}=\frac{6}{-6}
=-1
$