0=24x+6x^2+1

Solution for 0=24x+6x^2+1 equation:

0=24x+6x^2+1

We move all terms to the left:

0-(24x+6x^2+1)=0

We add all the numbers together, and all the variables

-(24x+6x^2+1)=0

We get rid of parentheses

-6x^2-24x-1=0

a = -6; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·(-6)·(-1)
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{138}}{2*-6}=\frac{24-2\sqrt{138}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{138}}{2*-6}=\frac{24+2\sqrt{138}}{-12}
$