84/r+315/r+7=399r=

Solution for 84/r+315/r+7=399r= equation:

84/r+315/r+7=399r=

We move all terms to the left:

84/r+315/r+7-(399r)=0


Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

-399r+84/r+315/r+7=0

We multiply all the terms by the denominator


-399r*r+7*r+84+315=0

We add all the numbers together, and all the variables

7r-399r*r+399=0

Wy multiply elements

-399r^2+7r+399=0

a = -399; b = 7; c = +399;
Δ = b2-4ac
Δ = 72-4·(-399)·399
Δ = 636853
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{636853}=\sqrt{49*12997}=\sqrt{49}*\sqrt{12997}=7\sqrt{12997}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7\sqrt{12997}}{2*-399}=\frac{-7-7\sqrt{12997}}{-798}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7\sqrt{12997}}{2*-399}=\frac{-7+7\sqrt{12997}}{-798}
$