x(x+1)=24.75

Solution for x(x+1)=24.75 equation:

x(x+1)=24.75

We move all terms to the left:

x(x+1)-(24.75)=0

We add all the numbers together, and all the variables

x(x+1)-24.75=0

We multiply parentheses

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