(x(x+1))=3.25

Solution for (x(x+1))=3.25 equation:

(x(x+1))=3.25

We move all terms to the left:

(x(x+1))-(3.25)=0

We add all the numbers together, and all the variables

(x(x+1))-3.25=0


We calculate terms in parentheses: +(x(x+1)), so:

x(x+1)

We multiply parentheses

x^2+x

Back to the equation:

+(x^2+x)


We get rid of parentheses

x^2+x-3.25=0

a = 1; b = 1; c = -3.25;
Δ = b2-4ac
Δ = 12-4·1·(-3.25)
Δ = 14
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{14}}{2*1}=\frac{-1-\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{14}}{2*1}=\frac{-1+\sqrt{14}}{2}
$