2x(x+8)=-2(9x-4)+6x

Solution for 2x(x+8)=-2(9x-4)+6x equation:

2x(x+8)=-2(9x-4)+6x

We move all terms to the left:

2x(x+8)-(-2(9x-4)+6x)=0

We multiply parentheses

2x^2+16x-(-2(9x-4)+6x)=0


We calculate terms in parentheses: -(-2(9x-4)+6x), so:

-2(9x-4)+6x

We add all the numbers together, and all the variables

6x-2(9x-4)

We multiply parentheses

6x-18x+8

We add all the numbers together, and all the variables

-12x+8

Back to the equation:

-(-12x+8)


We get rid of parentheses

2x^2+16x+12x-8=0

We add all the numbers together, and all the variables

2x^2+28x-8=0

a = 2; b = 28; c = -8;
Δ = b2-4ac
Δ = 282-4·2·(-8)
Δ = 848
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:

$\sqrt{\Delta}=\sqrt{848}=\sqrt{16*53}=\sqrt{16}*\sqrt{53}=4\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{53}}{2*2}=\frac{-28-4\sqrt{53}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{53}}{2*2}=\frac{-28+4\sqrt{53}}{4}
$