0=3x^2-45x-42

Solution for 0=3x^2-45x-42 equation:

0=3x^2-45x-42

We move all terms to the left:

0-(3x^2-45x-42)=0

We add all the numbers together, and all the variables

-(3x^2-45x-42)=0

We get rid of parentheses

-3x^2+45x+42=0

a = -3; b = 45; c = +42;
Δ = b2-4ac
Δ = 452-4·(-3)·42
Δ = 2529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2529}=\sqrt{9*281}=\sqrt{9}*\sqrt{281}=3\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{281}}{2*-3}=\frac{-45-3\sqrt{281}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{281}}{2*-3}=\frac{-45+3\sqrt{281}}{-6}
$