3x+7x(x-2)=6

Solution for 3x+7x(x-2)=6 equation:

3x+7x(x-2)=6

We move all terms to the left:

3x+7x(x-2)-(6)=0

We multiply parentheses

7x^2+3x-14x-6=0

We add all the numbers together, and all the variables

7x^2-11x-6=0

a = 7; b = -11; c = -6;
Δ = b2-4ac
Δ = -112-4·7·(-6)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-17}{2*7}=\frac{-6}{14}
=-3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*7}=\frac{28}{14}
=2
$