(3x+2)(x-1)=7-7x

Solution for (3x+2)(x-1)=7-7x equation:

(3x+2)(x-1)=7-7x

We move all terms to the left:

(3x+2)(x-1)-(7-7x)=0

We add all the numbers together, and all the variables

(3x+2)(x-1)-(-7x+7)=0

We get rid of parentheses

(3x+2)(x-1)+7x-7=0

We multiply parentheses ..

(+3x^2-3x+2x-2)+7x-7=0

We get rid of parentheses

3x^2-3x+2x+7x-2-7=0

We add all the numbers together, and all the variables

3x^2+6x-9=0

a = 3; b = 6; c = -9;
Δ = b2-4ac
Δ = 62-4·3·(-9)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*3}=\frac{6}{6}
=1
$