-24b^2+15b+16b=10

Solution for -24b^2+15b+16b=10 equation:

-24b^2+15b+16b=10

We move all terms to the left:

-24b^2+15b+16b-(10)=0

We add all the numbers together, and all the variables

-24b^2+31b-10=0

a = -24; b = 31; c = -10;
Δ = b2-4ac
Δ = 312-4·(-24)·(-10)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-1}{2*-24}=\frac{-32}{-48}
=2/3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+1}{2*-24}=\frac{-30}{-48}
=5/8
$