0=13b^2+58b+24

Solution for 0=13b^2+58b+24 equation:

0=13b^2+58b+24

We move all terms to the left:

0-(13b^2+58b+24)=0

We add all the numbers together, and all the variables

-(13b^2+58b+24)=0

We get rid of parentheses

-13b^2-58b-24=0

a = -13; b = -58; c = -24;
Δ = b2-4ac
Δ = -582-4·(-13)·(-24)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-46}{2*-13}=\frac{12}{-26}
=-6/13
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+46}{2*-13}=\frac{104}{-26}
=-4
$