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

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

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

We move all terms to the left:

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


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

5u(u+8)+u

We add all the numbers together, and all the variables

u+5u(u+8)

We multiply parentheses

5u^2+u+40u

We add all the numbers together, and all the variables

5u^2+41u

Back to the equation:

-(5u^2+41u)


We get rid of parentheses

-5u^2-41u-23=0

a = -5; b = -41; c = -23;
Δ = b2-4ac
Δ = -412-4·(-5)·(-23)
Δ = 1221
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-\sqrt{1221}}{2*-5}=\frac{41-\sqrt{1221}}{-10}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{1221}}{2*-5}=\frac{41+\sqrt{1221}}{-10}
$