2x(x+3)=4x(x-1)

Solution for 2x(x+3)=4x(x-1) equation:

2x(x+3)=4x(x-1)

We move all terms to the left:

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

We multiply parentheses

2x^2+6x-(4x(x-1))=0


We calculate terms in parentheses: -(4x(x-1)), so:

4x(x-1)

We multiply parentheses

4x^2-4x

Back to the equation:

-(4x^2-4x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+10x=0

a = -2; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-2)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-2}=\frac{0}{-4}
=0
$