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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

4(x*x+6)

We multiply parentheses

4x^2+24

Back to the equation:

-(4x^2+24)


We get rid of parentheses

8x^2-4x^2+2x-24=0

We add all the numbers together, and all the variables

4x^2+2x-24=0

a = 4; b = 2; c = -24;
Δ = b2-4ac
Δ = 22-4·4·(-24)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{97}}{2*4}=\frac{-2-2\sqrt{97}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{97}}{2*4}=\frac{-2+2\sqrt{97}}{8}
$