2x(x)(x-3)=42

Solution for 2x(x)(x-3)=42 equation:

2x(x)(x-3)=42

We move all terms to the left:

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

We multiply parentheses

2x^2-6x-42=0

a = 2; b = -6; c = -42;
Δ = b2-4ac
Δ = -62-4·2·(-42)
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{93}}{2*2}=\frac{6-2\sqrt{93}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{93}}{2*2}=\frac{6+2\sqrt{93}}{4}
$