-4u(u+5)-3(u+5)=0

Solution for -4u(u+5)-3(u+5)=0 equation:

-4u(u+5)-3(u+5)=0

We multiply parentheses

-4u^2-20u-3u-15=0

We add all the numbers together, and all the variables

-4u^2-23u-15=0

a = -4; b = -23; c = -15;
Δ = b2-4ac
Δ = -232-4·(-4)·(-15)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-17}{2*-4}=\frac{6}{-8}
=-3/4
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+17}{2*-4}=\frac{40}{-8}
=-5
$