0.75/(x+1)=x

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

0.75/(x+1)=x

We move all terms to the left:

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


Domain of the equation: (x+1)!=0

We move all terms containing x to the left, all other terms to the right

x!=-1

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We multiply parentheses

-x^2-x+0.75=0

We add all the numbers together, and all the variables

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