-23=5u(u+8)+2u

Solution for -23=5u(u+8)+2u equation:

-23=5u(u+8)+2u

We move all terms to the left:

-23-(5u(u+8)+2u)=0


We calculate terms in parentheses: -(5u(u+8)+2u), so:

5u(u+8)+2u

We add all the numbers together, and all the variables

2u+5u(u+8)

We multiply parentheses

5u^2+2u+40u

We add all the numbers together, and all the variables

5u^2+42u

Back to the equation:

-(5u^2+42u)


We get rid of parentheses

-5u^2-42u-23=0

a = -5; b = -42; c = -23;
Δ = b2-4ac
Δ = -422-4·(-5)·(-23)
Δ = 1304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1304}=\sqrt{4*326}=\sqrt{4}*\sqrt{326}=2\sqrt{326}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{326}}{2*-5}=\frac{42-2\sqrt{326}}{-10}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{326}}{2*-5}=\frac{42+2\sqrt{326}}{-10}
$