6x(x+2)=42

Solution for 6x(x+2)=42 equation:

6x(x+2)=42

We move all terms to the left:

6x(x+2)-(42)=0

We multiply parentheses

6x^2+12x-42=0

a = 6; b = 12; c = -42;
Δ = b2-4ac
Δ = 122-4·6·(-42)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-24\sqrt{2}}{2*6}=\frac{-12-24\sqrt{2}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24\sqrt{2}}{2*6}=\frac{-12+24\sqrt{2}}{12}
$