x2+9x=20.25

Solution for x2+9x=20.25 equation:

x2+9x=20.25

We move all terms to the left:

x2+9x-(20.25)=0

We add all the numbers together, and all the variables

x^2+9x-20.25=0

a = 1; b = 9; c = -20.25;
Δ = b2-4ac
Δ = 92-4·1·(-20.25)
Δ = 162
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{162}=\sqrt{81*2}=\sqrt{81}*\sqrt{2}=9\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9\sqrt{2}}{2*1}=\frac{-9-9\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9\sqrt{2}}{2*1}=\frac{-9+9\sqrt{2}}{2}
$