4x(9-2x)=4

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

4x(9-2x)=4

We move all terms to the left:

4x(9-2x)-(4)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

-8x^2+36x-4=0

a = -8; b = 36; c = -4;
Δ = b2-4ac
Δ = 362-4·(-8)·(-4)
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{73}}{2*-8}=\frac{-36-4\sqrt{73}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{73}}{2*-8}=\frac{-36+4\sqrt{73}}{-16}
$