3/2r+4-5r/r-1=0

Solution for 3/2r+4-5r/r-1=0 equation:

3/2r+4-5r/r-1=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R



Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

3/2r-5r/r+3=0

We calculate fractions


(-10r^2)/2r^2+3r/2r^2+3=0

We multiply all the terms by the denominator


(-10r^2)+3r+3*2r^2=0

Wy multiply elements

(-10r^2)+6r^2+3r=0

We get rid of parentheses

-10r^2+6r^2+3r=0

We add all the numbers together, and all the variables

-4r^2+3r=0

a = -4; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-4)·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*-4}=\frac{-6}{-8}
=3/4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-4}=\frac{0}{-8}
=0
$