x2-5x-74.75=0

Solution for x2-5x-74.75=0 equation:

x2-5x-74.75=0

We add all the numbers together, and all the variables

x^2-5x-74.75=0

a = 1; b = -5; c = -74.75;
Δ = b2-4ac
Δ = -52-4·1·(-74.75)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-18}{2*1}=\frac{-13}{2}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+18}{2*1}=\frac{23}{2}
=11+1/2
$