0=2b^2-4b-24

Solution for 0=2b^2-4b-24 equation:

0=2b^2-4b-24

We move all terms to the left:

0-(2b^2-4b-24)=0

We add all the numbers together, and all the variables

-(2b^2-4b-24)=0

We get rid of parentheses

-2b^2+4b+24=0

a = -2; b = 4; c = +24;
Δ = b2-4ac
Δ = 42-4·(-2)·24
Δ = 208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{13}}{2*-2}=\frac{-4-4\sqrt{13}}{-4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{13}}{2*-2}=\frac{-4+4\sqrt{13}}{-4}
$