6(x-4)=48x+6(x^2+2)

Solution for 6(x-4)=48x+6(x^2+2) equation:

6(x-4)=48x+6(x^2+2)

We move all terms to the left:

6(x-4)-(48x+6(x^2+2))=0

We multiply parentheses

6x-(48x+6(x^2+2))-24=0


We calculate terms in parentheses: -(48x+6(x^2+2)), so:

48x+6(x^2+2)

We multiply parentheses

6x^2+48x+12

Back to the equation:

-(6x^2+48x+12)


We get rid of parentheses

-6x^2+6x-48x-12-24=0

We add all the numbers together, and all the variables

-6x^2-42x-36=0

a = -6; b = -42; c = -36;
Δ = b2-4ac
Δ = -422-4·(-6)·(-36)
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*-6}=\frac{12}{-12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+30}{2*-6}=\frac{72}{-12}
=-6
$