6x+6=16x^2+8x+1

Solution for 6x+6=16x^2+8x+1 equation:

6x+6=16x^2+8x+1

We move all terms to the left:

6x+6-(16x^2+8x+1)=0

We get rid of parentheses

-16x^2+6x-8x-1+6=0

We add all the numbers together, and all the variables

-16x^2-2x+5=0

a = -16; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-16)·5
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-18}{2*-16}=\frac{-16}{-32}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+18}{2*-16}=\frac{20}{-32}
=-5/8
$