0=5w^2-7w-24

Solution for 0=5w^2-7w-24 equation:

0=5w^2-7w-24

We move all terms to the left:

0-(5w^2-7w-24)=0

We add all the numbers together, and all the variables

-(5w^2-7w-24)=0

We get rid of parentheses

-5w^2+7w+24=0

a = -5; b = 7; c = +24;
Δ = b2-4ac
Δ = 72-4·(-5)·24
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-23}{2*-5}=\frac{-30}{-10}
=+3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+23}{2*-5}=\frac{16}{-10}
=-1+3/5
$