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

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

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

We move all terms to the left:

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


Domain of the equation: 4r!=0

r!=0/4

r!=0

r∈R



Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R


We add all the numbers together, and all the variables

3/4r+1/2r-12=0

We calculate fractions


6r/8r^2+4r/8r^2-12=0

We multiply all the terms by the denominator


6r+4r-12*8r^2=0

We add all the numbers together, and all the variables

10r-12*8r^2=0

Wy multiply elements

-96r^2+10r=0

a = -96; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-96)·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*-96}=\frac{-20}{-192}
=5/48
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-96}=\frac{0}{-192}
=0
$