3(7+x)x=2

Solution for 3(7+x)x=2 equation:

3(7+x)x=2

We move all terms to the left:

3(7+x)x-(2)=0

We add all the numbers together, and all the variables

3(x+7)x-2=0

We multiply parentheses

3x^2+21x-2=0

a = 3; b = 21; c = -2;
Δ = b2-4ac
Δ = 212-4·3·(-2)
Δ = 465
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{465}}{2*3}=\frac{-21-\sqrt{465}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{465}}{2*3}=\frac{-21+\sqrt{465}}{6}
$