12+2x=-16x^2+24+6

Solution for 12+2x=-16x^2+24+6 equation:

12+2x=-16x^2+24+6

We move all terms to the left:

12+2x-(-16x^2+24+6)=0

We get rid of parentheses

16x^2+2x-24-6+12=0

We add all the numbers together, and all the variables

16x^2+2x-18=0

a = 16; b = 2; c = -18;
Δ = b2-4ac
Δ = 22-4·16·(-18)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-34}{2*16}=\frac{-36}{32}
=-1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+34}{2*16}=\frac{32}{32}
=1
$