4/3r-6=3/4r

Solution for 4/3r-6=3/4r equation:

4/3r-6=3/4r

We move all terms to the left:

4/3r-6-(3/4r)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R



Domain of the equation: 4r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

4/3r-(+3/4r)-6=0

We get rid of parentheses

4/3r-3/4r-6=0

We calculate fractions


16r/12r^2+(-9r)/12r^2-6=0

We multiply all the terms by the denominator


16r+(-9r)-6*12r^2=0

Wy multiply elements

-72r^2+16r+(-9r)=0

We get rid of parentheses

-72r^2+16r-9r=0

We add all the numbers together, and all the variables

-72r^2+7r=0

a = -72; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-72)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-72}=\frac{-14}{-144}
=7/72
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-72}=\frac{0}{-144}
=0
$