3x(14+2x)=x

Solution for 3x(14+2x)=x equation:

3x(14+2x)=x

We move all terms to the left:

3x(14+2x)-(x)=0

We add all the numbers together, and all the variables

3x(2x+14)-x=0

We add all the numbers together, and all the variables

-1x+3x(2x+14)=0

We multiply parentheses

6x^2-1x+42x=0

We add all the numbers together, and all the variables

6x^2+41x=0

a = 6; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·6·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*6}=\frac{-82}{12}
=-6+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*6}=\frac{0}{12}
=0
$