4x(5x+45)=4

Solution for 4x(5x+45)=4 equation:

4x(5x+45)=4

We move all terms to the left:

4x(5x+45)-(4)=0

We multiply parentheses

20x^2+180x-4=0

a = 20; b = 180; c = -4;
Δ = b2-4ac
Δ = 1802-4·20·(-4)
Δ = 32720
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:

$\sqrt{\Delta}=\sqrt{32720}=\sqrt{16*2045}=\sqrt{16}*\sqrt{2045}=4\sqrt{2045}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-4\sqrt{2045}}{2*20}=\frac{-180-4\sqrt{2045}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+4\sqrt{2045}}{2*20}=\frac{-180+4\sqrt{2045}}{40}
$