1/2r+5=3/4r-11

Solution for 1/2r+5=3/4r-11 equation:

1/2r+5=3/4r-11

We move all terms to the left:

1/2r+5-(3/4r-11)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R



Domain of the equation: 4r-11)!=0

r∈R


We get rid of parentheses

1/2r-3/4r+11+5=0

We calculate fractions


4r/8r^2+(-6r)/8r^2+11+5=0

We add all the numbers together, and all the variables

4r/8r^2+(-6r)/8r^2+16=0

We multiply all the terms by the denominator


4r+(-6r)+16*8r^2=0

Wy multiply elements

128r^2+4r+(-6r)=0

We get rid of parentheses

128r^2+4r-6r=0

We add all the numbers together, and all the variables

128r^2-2r=0

a = 128; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·128·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*128}=\frac{0}{256}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*128}=\frac{4}{256}
=1/64
$