x^2-x-24.75=0

Solution for x^2-x-24.75=0 equation:

x^2-x-24.75=0

We add all the numbers together, and all the variables

x^2-1x-24.75=0

a = 1; b = -1; c = -24.75;
Δ = b2-4ac
Δ = -12-4·1·(-24.75)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-10}{2*1}=\frac{-9}{2}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+10}{2*1}=\frac{11}{2}
=5+1/2
$