2x(2x+8)=2x(3x-1)

Solution for 2x(2x+8)=2x(3x-1) equation:

2x(2x+8)=2x(3x-1)

We move all terms to the left:

2x(2x+8)-(2x(3x-1))=0

We multiply parentheses

4x^2+16x-(2x(3x-1))=0


We calculate terms in parentheses: -(2x(3x-1)), so:

2x(3x-1)

We multiply parentheses

6x^2-2x

Back to the equation:

-(6x^2-2x)


We get rid of parentheses

4x^2-6x^2+16x+2x=0

We add all the numbers together, and all the variables

-2x^2+18x=0

a = -2; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-2)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-2}=\frac{-36}{-4}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-2}=\frac{0}{-4}
=0
$