6x(x-7)=3x-12

Solution for 6x(x-7)=3x-12 equation:

6x(x-7)=3x-12

We move all terms to the left:

6x(x-7)-(3x-12)=0

We multiply parentheses

6x^2-42x-(3x-12)=0

We get rid of parentheses

6x^2-42x-3x+12=0

We add all the numbers together, and all the variables

6x^2-45x+12=0

a = 6; b = -45; c = +12;
Δ = b2-4ac
Δ = -452-4·6·12
Δ = 1737
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1737}=\sqrt{9*193}=\sqrt{9}*\sqrt{193}=3\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{193}}{2*6}=\frac{45-3\sqrt{193}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{193}}{2*6}=\frac{45+3\sqrt{193}}{12}
$