0=3x^2-6x-45

Solution for 0=3x^2-6x-45 equation:

0=3x^2-6x-45

We move all terms to the left:

0-(3x^2-6x-45)=0

We add all the numbers together, and all the variables

-(3x^2-6x-45)=0

We get rid of parentheses

-3x^2+6x+45=0

a = -3; b = 6; c = +45;
Δ = b2-4ac
Δ = 62-4·(-3)·45
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{-(6)-24}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+24}{2*-3}=\frac{18}{-6}
=-3
$