12x(x+4)=6(x-3)

Solution for 12x(x+4)=6(x-3) equation:

12x(x+4)=6(x-3)

We move all terms to the left:

12x(x+4)-(6(x-3))=0

We multiply parentheses

12x^2+48x-(6(x-3))=0


We calculate terms in parentheses: -(6(x-3)), so:

6(x-3)

We multiply parentheses

6x-18

Back to the equation:

-(6x-18)


We get rid of parentheses

12x^2+48x-6x+18=0

We add all the numbers together, and all the variables

12x^2+42x+18=0

a = 12; b = 42; c = +18;
Δ = b2-4ac
Δ = 422-4·12·18
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-30}{2*12}=\frac{-72}{24}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+30}{2*12}=\frac{-12}{24}
=-1/2
$