u^2-3u-2.25=0

Solution for u^2-3u-2.25=0 equation:

u^2-3u-2.25=0

a = 1; b = -3; c = -2.25;
Δ = b2-4ac
Δ = -32-4·1·(-2.25)
Δ = 18
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18}=\sqrt{9*2}=\sqrt{9}*\sqrt{2}=3\sqrt{2}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{2}}{2*1}=\frac{3-3\sqrt{2}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{2}}{2*1}=\frac{3+3\sqrt{2}}{2}
$