-3x(x-7)=42-6x

Solution for -3x(x-7)=42-6x equation:

-3x(x-7)=42-6x

We move all terms to the left:

-3x(x-7)-(42-6x)=0

We add all the numbers together, and all the variables

-3x(x-7)-(-6x+42)=0

We multiply parentheses

-3x^2+21x-(-6x+42)=0

We get rid of parentheses

-3x^2+21x+6x-42=0

We add all the numbers together, and all the variables

-3x^2+27x-42=0

a = -3; b = 27; c = -42;
Δ = b2-4ac
Δ = 272-4·(-3)·(-42)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-15}{2*-3}=\frac{-42}{-6}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+15}{2*-3}=\frac{-12}{-6}
=+2
$