84b^2+92b=-24

Solution for 84b^2+92b=-24 equation:

84b^2+92b=-24

We move all terms to the left:

84b^2+92b-(-24)=0

We add all the numbers together, and all the variables

84b^2+92b+24=0

a = 84; b = 92; c = +24;
Δ = b2-4ac
Δ = 922-4·84·24
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-20}{2*84}=\frac{-112}{168}
=-2/3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+20}{2*84}=\frac{-72}{168}
=-3/7
$