6x(x+4)=42

Solution for 6x(x+4)=42 equation:

6x(x+4)=42

We move all terms to the left:

6x(x+4)-(42)=0

We multiply parentheses

6x^2+24x-42=0

a = 6; b = 24; c = -42;
Δ = b2-4ac
Δ = 242-4·6·(-42)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{11}}{2*6}=\frac{-24-12\sqrt{11}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{11}}{2*6}=\frac{-24+12\sqrt{11}}{12}
$