4u^2+2=9u

Solution for 4u^2+2=9u equation:

4u^2+2=9u

We move all terms to the left:

4u^2+2-(9u)=0

a = 4; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·4·2
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7}{2*4}=\frac{2}{8}
=1/4
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*4}=\frac{16}{8}
=2
$