6-3/4r=1/2r+1

Solution for 6-3/4r=1/2r+1 equation:

6-3/4r=1/2r+1

We move all terms to the left:

6-3/4r-(1/2r+1)=0


Domain of the equation: 4r!=0

r!=0/4

r!=0

r∈R



Domain of the equation: 2r+1)!=0

r∈R


We get rid of parentheses

-3/4r-1/2r-1+6=0

We calculate fractions


(-6r)/8r^2+(-4r)/8r^2-1+6=0

We add all the numbers together, and all the variables

(-6r)/8r^2+(-4r)/8r^2+5=0

We multiply all the terms by the denominator


(-6r)+(-4r)+5*8r^2=0

Wy multiply elements

40r^2+(-6r)+(-4r)=0

We get rid of parentheses

40r^2-6r-4r=0

We add all the numbers together, and all the variables

40r^2-10r=0

a = 40; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·40·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*40}=\frac{0}{80}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*40}=\frac{20}{80}
=1/4
$