12+26x-16x^2=-12

Solution for 12+26x-16x^2=-12 equation:

12+26x-16x^2=-12

We move all terms to the left:

12+26x-16x^2-(-12)=0

We add all the numbers together, and all the variables

-16x^2+26x+24=0

a = -16; b = 26; c = +24;
Δ = b2-4ac
Δ = 262-4·(-16)·24
Δ = 2212
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:

$\sqrt{\Delta}=\sqrt{2212}=\sqrt{4*553}=\sqrt{4}*\sqrt{553}=2\sqrt{553}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{553}}{2*-16}=\frac{-26-2\sqrt{553}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{553}}{2*-16}=\frac{-26+2\sqrt{553}}{-32}
$