6x(3x-7)=x

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

6x(3x-7)=x

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x+6x(3x-7)=0

We multiply parentheses

18x^2-1x-42x=0

We add all the numbers together, and all the variables

18x^2-43x=0

a = 18; b = -43; c = 0;
Δ = b2-4ac
Δ = -432-4·18·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-43}{2*18}=\frac{0}{36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+43}{2*18}=\frac{86}{36}
=2+7/18
$