4x(x+2)+6=2(3x+8)

Solution for 4x(x+2)+6=2(3x+8) equation:

4x(x+2)+6=2(3x+8)

We move all terms to the left:

4x(x+2)+6-(2(3x+8))=0

We multiply parentheses

4x^2+8x-(2(3x+8))+6=0


We calculate terms in parentheses: -(2(3x+8)), so:

2(3x+8)

We multiply parentheses

6x+16

Back to the equation:

-(6x+16)


We get rid of parentheses

4x^2+8x-6x-16+6=0

We add all the numbers together, and all the variables

4x^2+2x-10=0

a = 4; b = 2; c = -10;
Δ = b2-4ac
Δ = 22-4·4·(-10)
Δ = 164
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{41}}{2*4}=\frac{-2-2\sqrt{41}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{41}}{2*4}=\frac{-2+2\sqrt{41}}{8}
$