7r+3=55/r=

Solution for 7r+3=55/r= equation:

7r+3=55/r=

We move all terms to the left:

7r+3-(55/r)=0


Domain of the equation: r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

7r-(+55/r)+3=0

We get rid of parentheses

7r-55/r+3=0

We multiply all the terms by the denominator


7r*r+3*r-55=0

We add all the numbers together, and all the variables

3r+7r*r-55=0

Wy multiply elements

7r^2+3r-55=0

a = 7; b = 3; c = -55;
Δ = b2-4ac
Δ = 32-4·7·(-55)
Δ = 1549
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{1549}}{2*7}=\frac{-3-\sqrt{1549}}{14}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{1549}}{2*7}=\frac{-3+\sqrt{1549}}{14}
$