4x^2-12x-9=16

Solution for 4x^2-12x-9=16 equation:

4x^2-12x-9=16

We move all terms to the left:

4x^2-12x-9-(16)=0

We add all the numbers together, and all the variables

4x^2-12x-25=0

a = 4; b = -12; c = -25;
Δ = b2-4ac
Δ = -122-4·4·(-25)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{34}}{2*4}=\frac{12-4\sqrt{34}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{34}}{2*4}=\frac{12+4\sqrt{34}}{8}
$