7/2r-1=2r+5

Solution for 7/2r-1=2r+5 equation:

7/2r-1=2r+5

We move all terms to the left:

7/2r-1-(2r+5)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R


We get rid of parentheses

7/2r-2r-5-1=0

We multiply all the terms by the denominator


-2r*2r-5*2r-1*2r+7=0

Wy multiply elements

-4r^2-10r-2r+7=0

We add all the numbers together, and all the variables

-4r^2-12r+7=0

a = -4; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·(-4)·7
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-16}{2*-4}=\frac{-4}{-8}
=1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+16}{2*-4}=\frac{28}{-8}
=-3+1/2
$