2x^2-16x-27=-12

Solution for 2x^2-16x-27=-12 equation:

2x^2-16x-27=-12

We move all terms to the left:

2x^2-16x-27-(-12)=0

We add all the numbers together, and all the variables

2x^2-16x-15=0

a = 2; b = -16; c = -15;
Δ = b2-4ac
Δ = -162-4·2·(-15)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{94}}{2*2}=\frac{16-2\sqrt{94}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{94}}{2*2}=\frac{16+2\sqrt{94}}{4}
$