x(x+1)=3.75

Solution for x(x+1)=3.75 equation:

x(x+1)=3.75

We move all terms to the left:

x(x+1)-(3.75)=0

We add all the numbers together, and all the variables

x(x+1)-3.75=0

We multiply parentheses

x^2+x-3.75=0

a = 1; b = 1; c = -3.75;
Δ = b2-4ac
Δ = 12-4·1·(-3.75)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-4}{2*1}=\frac{-5}{2}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+4}{2*1}=\frac{3}{2}
=1+1/2
$