2a^2-22a=-30.25

Solution for 2a^2-22a=-30.25 equation:

2a^2-22a=-30.25

We move all terms to the left:

2a^2-22a-(-30.25)=0

We add all the numbers together, and all the variables

2a^2-22a+30.25=0

a = 2; b = -22; c = +30.25;
Δ = b2-4ac
Δ = -222-4·2·30.25
Δ = 242
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{242}=\sqrt{121*2}=\sqrt{121}*\sqrt{2}=11\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-11\sqrt{2}}{2*2}=\frac{22-11\sqrt{2}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+11\sqrt{2}}{2*2}=\frac{22+11\sqrt{2}}{4}
$