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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

3x(x+4)

We multiply parentheses

3x^2+12x

Back to the equation:

-(3x^2+12x)


We get rid of parentheses

2x^2-3x^2-2x-12x=0

We add all the numbers together, and all the variables

-1x^2-14x=0

a = -1; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-1)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-1}=\frac{28}{-2}
=-14
$