6x+24=2x(x+4)

Solution for 6x+24=2x(x+4) equation:

6x+24=2x(x+4)

We move all terms to the left:

6x+24-(2x(x+4))=0


We calculate terms in parentheses: -(2x(x+4)), so:

2x(x+4)

We multiply parentheses

2x^2+8x

Back to the equation:

-(2x^2+8x)


We get rid of parentheses

-2x^2+6x-8x+24=0

We add all the numbers together, and all the variables

-2x^2-2x+24=0

a = -2; b = -2; c = +24;
Δ = b2-4ac
Δ = -22-4·(-2)·24
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{-(-2)-14}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*-2}=\frac{16}{-4}
=-4
$