2/(x+1)=4x-3

Solution for 2/(x+1)=4x-3 equation:

2/(x+1)=4x-3

We move all terms to the left:

2/(x+1)-(4x-3)=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 get rid of parentheses

2/(x+1)-4x+3=0

We multiply all the terms by the denominator


-4x*(x+1)+3*(x+1)+2=0

We multiply parentheses

-4x^2-4x+3x+3+2=0

We add all the numbers together, and all the variables

-4x^2-1x+5=0

a = -4; b = -1; c = +5;
Δ = b2-4ac
Δ = -12-4·(-4)·5
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*-4}=\frac{10}{-8}
=-1+1/4
$