5(x-2)=(3x+2)(x-2)

Solution for 5(x-2)=(3x+2)(x-2) equation:

5(x-2)=(3x+2)(x-2)

We move all terms to the left:

5(x-2)-((3x+2)(x-2))=0

We multiply parentheses

5x-((3x+2)(x-2))-10=0

We multiply parentheses ..

-((+3x^2-6x+2x-4))+5x-10=0


We calculate terms in parentheses: -((+3x^2-6x+2x-4)), so:

(+3x^2-6x+2x-4)

We get rid of parentheses

3x^2-6x+2x-4

We add all the numbers together, and all the variables

3x^2-4x-4

Back to the equation:

-(3x^2-4x-4)


We add all the numbers together, and all the variables

5x-(3x^2-4x-4)-10=0

We get rid of parentheses

-3x^2+5x+4x+4-10=0

We add all the numbers together, and all the variables

-3x^2+9x-6=0

a = -3; b = 9; c = -6;
Δ = b2-4ac
Δ = 92-4·(-3)·(-6)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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