2x-8(4+2x)=14x(2x-9)2

Solution for 2x-8(4+2x)=14x(2x-9)2 equation:

2x-8(4+2x)=14x(2x-9)2

We move all terms to the left:

2x-8(4+2x)-(14x(2x-9)2)=0

We add all the numbers together, and all the variables

2x-8(2x+4)-(14x(2x-9)2)=0

We multiply parentheses

2x-16x-(14x(2x-9)2)-32=0


We calculate terms in parentheses: -(14x(2x-9)2), so:

14x(2x-9)2

We multiply parentheses

56x^2-252x

Back to the equation:

-(56x^2-252x)


We add all the numbers together, and all the variables

-14x-(56x^2-252x)-32=0

We get rid of parentheses

-56x^2-14x+252x-32=0

We add all the numbers together, and all the variables

-56x^2+238x-32=0

a = -56; b = 238; c = -32;
Δ = b2-4ac
Δ = 2382-4·(-56)·(-32)
Δ = 49476
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:

$\sqrt{\Delta}=\sqrt{49476}=\sqrt{4*12369}=\sqrt{4}*\sqrt{12369}=2\sqrt{12369}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(238)-2\sqrt{12369}}{2*-56}=\frac{-238-2\sqrt{12369}}{-112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(238)+2\sqrt{12369}}{2*-56}=\frac{-238+2\sqrt{12369}}{-112}
$