27=4x(x+2)

Solution for 27=4x(x+2) equation:

27=4x(x+2)

We move all terms to the left:

27-(4x(x+2))=0


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

4x(x+2)

We multiply parentheses

4x^2+8x

Back to the equation:

-(4x^2+8x)


We get rid of parentheses

-4x^2-8x+27=0

a = -4; b = -8; c = +27;
Δ = b2-4ac
Δ = -82-4·(-4)·27
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{31}}{2*-4}=\frac{8-4\sqrt{31}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{31}}{2*-4}=\frac{8+4\sqrt{31}}{-8}
$