-3/2r+1+8/3r=37/30

Solution for -3/2r+1+8/3r=37/30 equation:

-3/2r+1+8/3r=37/30

We move all terms to the left:

-3/2r+1+8/3r-(37/30)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R



Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R


We add all the numbers together, and all the variables

-3/2r+8/3r+1-(+37/30)=0

We get rid of parentheses

-3/2r+8/3r+1-37/30=0

We calculate fractions


(-666r^2)/540r^2+(-810r)/540r^2+1440r/540r^2+1=0

We multiply all the terms by the denominator


(-666r^2)+(-810r)+1440r+1*540r^2=0

We add all the numbers together, and all the variables

(-666r^2)+1440r+(-810r)+1*540r^2=0

Wy multiply elements

(-666r^2)+540r^2+1440r+(-810r)=0

We get rid of parentheses

-666r^2+540r^2+1440r-810r=0

We add all the numbers together, and all the variables

-126r^2+630r=0

a = -126; b = 630; c = 0;
Δ = b2-4ac
Δ = 6302-4·(-126)·0
Δ = 396900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{396900}=630$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(630)-630}{2*-126}=\frac{-1260}{-252}
=+5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(630)+630}{2*-126}=\frac{0}{-252}
=0
$