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

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

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

We move all terms to the left:

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


Domain of the equation: 4r!=0

r!=0/4

r!=0

r∈R



Domain of the equation: 2r-1)!=0

r∈R


We multiply parentheses

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

We get rid of parentheses

3/4r+3r-2r+1-3=0

We multiply all the terms by the denominator


3r*4r-2r*4r+1*4r-3*4r+3=0

Wy multiply elements

12r^2-8r^2+4r-12r+3=0

We add all the numbers together, and all the variables

4r^2-8r+3=0

a = 4; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·4·3
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4}{2*4}=\frac{4}{8}
=1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4}{2*4}=\frac{12}{8}
=1+1/2
$