15u^2-8u+3=6u

Solution for 15u^2-8u+3=6u equation:

15u^2-8u+3=6u

We move all terms to the left:

15u^2-8u+3-(6u)=0

We add all the numbers together, and all the variables

15u^2-14u+3=0

a = 15; b = -14; c = +3;
Δ = b2-4ac
Δ = -142-4·15·3
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4}{2*15}=\frac{10}{30}
=1/3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4}{2*15}=\frac{18}{30}
=3/5
$