2x(x+1)=12(x+4)

Solution for 2x(x+1)=12(x+4) equation:

2x(x+1)=12(x+4)

We move all terms to the left:

2x(x+1)-(12(x+4))=0

We multiply parentheses

2x^2+2x-(12(x+4))=0


We calculate terms in parentheses: -(12(x+4)), so:

12(x+4)

We multiply parentheses

12x+48

Back to the equation:

-(12x+48)


We get rid of parentheses

2x^2+2x-12x-48=0

We add all the numbers together, and all the variables

2x^2-10x-48=0

a = 2; b = -10; c = -48;
Δ = b2-4ac
Δ = -102-4·2·(-48)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-22}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+22}{2*2}=\frac{32}{4}
=8
$