0.4w(6w-10)+1.5w=24.08

Solution for 0.4w(6w-10)+1.5w=24.08 equation:

0.4w(6w-10)+1.5w=24.08

We move all terms to the left:

0.4w(6w-10)+1.5w-(24.08)=0

We add all the numbers together, and all the variables

1.5w+0.4w(6w-10)-24.08=0

We multiply parentheses

0w^2+1.5w+0w-24.08=0

We add all the numbers together, and all the variables

w^2+2.5w-24.08=0

a = 1; b = 2.5; c = -24.08;
Δ = b2-4ac
Δ = 2.52-4·1·(-24.08)
Δ = 102.57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2.5)-\sqrt{102.57}}{2*1}=\frac{-2.5-\sqrt{102.57}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{102.57}}{2*1}=\frac{-2.5+\sqrt{102.57}}{2}
$