x(1+x)=0.75

Solution for x(1+x)=0.75 equation:

x(1+x)=0.75

We move all terms to the left:

x(1+x)-(0.75)=0

We add all the numbers together, and all the variables

x(x+1)-(0.75)=0

We add all the numbers together, and all the variables

x(x+1)-0.75=0

We multiply parentheses

x^2+x-0.75=0

a = 1; b = 1; c = -0.75;
Δ = b2-4ac
Δ = 12-4·1·(-0.75)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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