x^2-5x=18.5

Solution for x^2-5x=18.5 equation:

x^2-5x=18.5

We move all terms to the left:

x^2-5x-(18.5)=0

We add all the numbers together, and all the variables

x^2-5x-18.5=0

a = 1; b = -5; c = -18.5;
Δ = b2-4ac
Δ = -52-4·1·(-18.5)
Δ = 99
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:

$\sqrt{\Delta}=\sqrt{99}=\sqrt{9*11}=\sqrt{9}*\sqrt{11}=3\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{11}}{2*1}=\frac{5-3\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{11}}{2*1}=\frac{5+3\sqrt{11}}{2}
$