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

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

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

We move all terms to the left:

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

We multiply parentheses

7x^2-21x-(2x-6)=0

We get rid of parentheses

7x^2-21x-2x+6=0

We add all the numbers together, and all the variables

7x^2-23x+6=0

a = 7; b = -23; c = +6;
Δ = b2-4ac
Δ = -232-4·7·6
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-19}{2*7}=\frac{4}{14}
=2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+19}{2*7}=\frac{42}{14}
=3
$