-31=2u(u-8)-5u

Solution for -31=2u(u-8)-5u equation:

-31=2u(u-8)-5u

We move all terms to the left:

-31-(2u(u-8)-5u)=0


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

2u(u-8)-5u

We add all the numbers together, and all the variables

-5u+2u(u-8)

We multiply parentheses

2u^2-5u-16u

We add all the numbers together, and all the variables

2u^2-21u

Back to the equation:

-(2u^2-21u)


We get rid of parentheses

-2u^2+21u-31=0

a = -2; b = 21; c = -31;
Δ = b2-4ac
Δ = 212-4·(-2)·(-31)
Δ = 193
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{-(21)-\sqrt{193}}{2*-2}=\frac{-21-\sqrt{193}}{-4}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{193}}{2*-2}=\frac{-21+\sqrt{193}}{-4}
$