(5u-8)(4+u)=0

Solution for (5u-8)(4+u)=0 equation:

(5u-8)(4+u)=0

We add all the numbers together, and all the variables

(5u-8)(u+4)=0

We multiply parentheses ..

(+5u^2+20u-8u-32)=0

We get rid of parentheses

5u^2+20u-8u-32=0

We add all the numbers together, and all the variables

5u^2+12u-32=0

a = 5; b = 12; c = -32;
Δ = b2-4ac
Δ = 122-4·5·(-32)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-28}{2*5}=\frac{-40}{10}
=-4
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+28}{2*5}=\frac{16}{10}
=1+3/5
$