1/2r-3=34-3/4r

Solution for 1/2r-3=34-3/4r equation:

1/2r-3=34-3/4r

We move all terms to the left:

1/2r-3-(34-3/4r)=0


Domain of the equation: 2r!=0

r!=0/2

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

1/2r-(-3/4r+34)-3=0

We get rid of parentheses

1/2r+3/4r-34-3=0

We calculate fractions


4r/8r^2+6r/8r^2-34-3=0

We add all the numbers together, and all the variables

4r/8r^2+6r/8r^2-37=0

We multiply all the terms by the denominator


4r+6r-37*8r^2=0

We add all the numbers together, and all the variables

10r-37*8r^2=0

Wy multiply elements

-296r^2+10r=0

a = -296; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-296)·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*-296}=\frac{-20}{-592}
=5/148
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-296}=\frac{0}{-592}
=0
$