x^2+8.5x+72.25=76.75

Solution for x^2+8.5x+72.25=76.75 equation:

x^2+8.5x+72.25=76.75

We move all terms to the left:

x^2+8.5x+72.25-(76.75)=0

We add all the numbers together, and all the variables

x^2+8.5x-4.5=0

a = 1; b = 8.5; c = -4.5;
Δ = b2-4ac
Δ = 8.52-4·1·(-4.5)
Δ = 90.25
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{-(8.5)-\sqrt{90.25}}{2*1}=\frac{-8.5-\sqrt{90.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8.5)+\sqrt{90.25}}{2*1}=\frac{-8.5+\sqrt{90.25}}{2}
$