4x^2+9x+20.25=21.25

Solution for 4x^2+9x+20.25=21.25 equation:

4x^2+9x+20.25=21.25

We move all terms to the left:

4x^2+9x+20.25-(21.25)=0

We add all the numbers together, and all the variables

4x^2+9x-1=0

a = 4; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·4·(-1)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{97}}{2*4}=\frac{-9-\sqrt{97}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{97}}{2*4}=\frac{-9+\sqrt{97}}{8}
$