3*u*u-5*u=-2*u

Solution for 3*u*u-5*u=-2*u equation:

3u*u-5u=-2u

We move all terms to the left:

3u*u-5u-(-2u)=0

We add all the numbers together, and all the variables

-5u+3u*u-(-2u)=0

Wy multiply elements

3u^2-5u-(-2u)=0

We get rid of parentheses

3u^2-5u+2u=0

We add all the numbers together, and all the variables

3u^2-3u=0

a = 3; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·3·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*3}=\frac{0}{6}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*3}=\frac{6}{6}
=1
$