x^2+17x+72.25=78.75

Solution for x^2+17x+72.25=78.75 equation:

x^2+17x+72.25=78.75

We move all terms to the left:

x^2+17x+72.25-(78.75)=0

We add all the numbers together, and all the variables

x^2+17x-6.5=0

a = 1; b = 17; c = -6.5;
Δ = b2-4ac
Δ = 172-4·1·(-6.5)
Δ = 315
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:

$\sqrt{\Delta}=\sqrt{315}=\sqrt{9*35}=\sqrt{9}*\sqrt{35}=3\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-3\sqrt{35}}{2*1}=\frac{-17-3\sqrt{35}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+3\sqrt{35}}{2*1}=\frac{-17+3\sqrt{35}}{2}
$