2(x+4)x=62(x+4)x=6

Solution for 2(x+4)x=62(x+4)x=6 equation:

2(x+4)x=62(x+4)x=6

We move all terms to the left:

2(x+4)x-(62(x+4)x)=0

We multiply parentheses

2x^2+8x-(62(x+4)x)=0


We calculate terms in parentheses: -(62(x+4)x), so:

62(x+4)x

We multiply parentheses

62x^2+248x

Back to the equation:

-(62x^2+248x)


We get rid of parentheses

2x^2-62x^2+8x-248x=0

We add all the numbers together, and all the variables

-60x^2-240x=0

a = -60; b = -240; c = 0;
Δ = b2-4ac
Δ = -2402-4·(-60)·0
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-240}{2*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+240}{2*-60}=\frac{480}{-120}
=-4
$