1/4r+1/7r=11

Solution for 1/4r+1/7r=11 equation:

1/4r+1/7r=11

We move all terms to the left:

1/4r+1/7r-(11)=0


Domain of the equation: 4r!=0

r!=0/4

r!=0

r∈R



Domain of the equation: 7r!=0

r!=0/7

r!=0

r∈R


We calculate fractions


7r/28r^2+4r/28r^2-11=0

We multiply all the terms by the denominator


7r+4r-11*28r^2=0

We add all the numbers together, and all the variables

11r-11*28r^2=0

Wy multiply elements

-308r^2+11r=0

a = -308; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-308)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-308}=\frac{-22}{-616}
=1/28
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-308}=\frac{0}{-616}
=0
$