7/2r=4/r+5

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

7/2r=4/r+5

We move all terms to the left:

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


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R



Domain of the equation: r+5)!=0

r∈R


We get rid of parentheses

7/2r-4/r-5=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-10r^2+7r+(-8r)=0

We get rid of parentheses

-10r^2+7r-8r=0

We add all the numbers together, and all the variables

-10r^2-1r=0

a = -10; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-10)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-10}=\frac{0}{-20}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-10}=\frac{2}{-20}
=-1/10
$