x(x+1)=31.50

Solution for x(x+1)=31.50 equation:

x(x+1)=31.50

We move all terms to the left:

x(x+1)-(31.50)=0

We add all the numbers together, and all the variables

x(x+1)-(31.5)=0

We add all the numbers together, and all the variables

x(x+1)-31.5=0

We multiply parentheses

x^2+x-31.5=0

a = 1; b = 1; c = -31.5;
Δ = b2-4ac
Δ = 12-4·1·(-31.5)
Δ = 127
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{127}}{2*1}=\frac{-1-\sqrt{127}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{127}}{2*1}=\frac{-1+\sqrt{127}}{2}
$