5u^2=9u-4

Solution for 5u^2=9u-4 equation:

5u^2=9u-4

We move all terms to the left:

5u^2-(9u-4)=0

We get rid of parentheses

5u^2-9u+4=0

a = 5; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·5·4
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-1}{2*5}=\frac{8}{10}
=4/5
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*5}=\frac{10}{10}
=1
$