3x2-6x-42=5x

Solution for 3x2-6x-42=5x equation:

3x^2-6x-42=5x

We move all terms to the left:

3x^2-6x-42-(5x)=0

We add all the numbers together, and all the variables

3x^2-11x-42=0

a = 3; b = -11; c = -42;
Δ = b2-4ac
Δ = -112-4·3·(-42)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-25}{2*3}=\frac{-14}{6}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+25}{2*3}=\frac{36}{6}
=6
$