10=u(17-3u)

Solution for 10=u(17-3u) equation:

10=u(17-3u)

We move all terms to the left:

10-(u(17-3u))=0

We add all the numbers together, and all the variables

-(u(-3u+17))+10=0


We calculate terms in parentheses: -(u(-3u+17)), so:

u(-3u+17)

We multiply parentheses

-3u^2+17u

Back to the equation:

-(-3u^2+17u)


We get rid of parentheses

3u^2-17u+10=0

a = 3; b = -17; c = +10;
Δ = b2-4ac
Δ = -172-4·3·10
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-13}{2*3}=\frac{4}{6}
=2/3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+13}{2*3}=\frac{30}{6}
=5
$