3x(x+2)-20=5(x-2)

Solution for 3x(x+2)-20=5(x-2) equation:

3x(x+2)-20=5(x-2)

We move all terms to the left:

3x(x+2)-20-(5(x-2))=0

We multiply parentheses

3x^2+6x-(5(x-2))-20=0


We calculate terms in parentheses: -(5(x-2)), so:

5(x-2)

We multiply parentheses

5x-10

Back to the equation:

-(5x-10)


We get rid of parentheses

3x^2+6x-5x+10-20=0

We add all the numbers together, and all the variables

3x^2+x-10=0

a = 3; b = 1; c = -10;
Δ = b2-4ac
Δ = 12-4·3·(-10)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*3}=\frac{10}{6}
=1+2/3
$