x^2+19x+90.25=216

Solution for x^2+19x+90.25=216 equation:

x^2+19x+90.25=216

We move all terms to the left:

x^2+19x+90.25-(216)=0

We add all the numbers together, and all the variables

x^2+19x-125.75=0

a = 1; b = 19; c = -125.75;
Δ = b2-4ac
Δ = 192-4·1·(-125.75)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-12\sqrt{6}}{2*1}=\frac{-19-12\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+12\sqrt{6}}{2*1}=\frac{-19+12\sqrt{6}}{2}
$