51/2r+2/3r=37

Solution for 51/2r+2/3r=37 equation:

51/2r+2/3r=37

We move all terms to the left:

51/2r+2/3r-(37)=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 calculate fractions


153r/6r^2+4r/6r^2-37=0

We multiply all the terms by the denominator


153r+4r-37*6r^2=0

We add all the numbers together, and all the variables

157r-37*6r^2=0

Wy multiply elements

-222r^2+157r=0

a = -222; b = 157; c = 0;
Δ = b2-4ac
Δ = 1572-4·(-222)·0
Δ = 24649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24649}=157$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(157)-157}{2*-222}=\frac{-314}{-444}
=157/222
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(157)+157}{2*-222}=\frac{0}{-444}
=0
$