5/2r+1=4/rr-7

Solution for 5/2r+1=4/rr-7 equation:

5/2r+1=4/rr-7

We move all terms to the left:

5/2r+1-(4/rr-7)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R



Domain of the equation: rr-7)!=0

r∈R


We get rid of parentheses

5/2r-4/rr+7+1=0

We calculate fractions


5r/2r^2+(-8r)/2r^2+7+1=0

We add all the numbers together, and all the variables

5r/2r^2+(-8r)/2r^2+8=0

We multiply all the terms by the denominator


5r+(-8r)+8*2r^2=0

Wy multiply elements

16r^2+5r+(-8r)=0

We get rid of parentheses

16r^2+5r-8r=0

We add all the numbers together, and all the variables

16r^2-3r=0

a = 16; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·16·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*16}=\frac{0}{32}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*16}=\frac{6}{32}
=3/16
$