4x^2+48x+20=9

Solution for 4x^2+48x+20=9 equation:

4x^2+48x+20=9

We move all terms to the left:

4x^2+48x+20-(9)=0

We add all the numbers together, and all the variables

4x^2+48x+11=0

a = 4; b = 48; c = +11;
Δ = b2-4ac
Δ = 482-4·4·11
Δ = 2128
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:

$\sqrt{\Delta}=\sqrt{2128}=\sqrt{16*133}=\sqrt{16}*\sqrt{133}=4\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{133}}{2*4}=\frac{-48-4\sqrt{133}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{133}}{2*4}=\frac{-48+4\sqrt{133}}{8}
$