26w+5w^2-24=0

Solution for 26w+5w^2-24=0 equation:

26w+5w^2-24=0

a = 5; b = 26; c = -24;
Δ = b2-4ac
Δ = 262-4·5·(-24)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-34}{2*5}=\frac{-60}{10}
=-6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+34}{2*5}=\frac{8}{10}
=4/5
$