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

Solution for (3-2x)(x+7)-(3-2x)(2x+1)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-2x^2-14x+3x+21)-(-2x+3)(2x+1)=0

We get rid of parentheses

-2x^2-14x+3x-(-2x+3)(2x+1)+21=0

We multiply parentheses ..

-2x^2-(-4x^2-2x+6x+3)-14x+3x+21=0

We add all the numbers together, and all the variables

-2x^2-(-4x^2-2x+6x+3)-11x+21=0

We get rid of parentheses

-2x^2+4x^2+2x-6x-11x-3+21=0

We add all the numbers together, and all the variables

2x^2-15x+18=0

a = 2; b = -15; c = +18;
Δ = b2-4ac
Δ = -152-4·2·18
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9}{2*2}=\frac{6}{4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9}{2*2}=\frac{24}{4}
=6
$