2r+49=-8(-r-5)J/2r+49=-8(-r-5)

Solution for 2r+49=-8(-r-5)J/2r+49=-8(-r-5) equation:

2r+49=-8(-r-5)/2r+49=-8(-r-5)

We move all terms to the left:

2r+49-(-8(-r-5)/2r+49)=0


Domain of the equation: 2r+49)!=0

r∈R


We add all the numbers together, and all the variables

2r-(-8(-1r-5)/2r+49)+49=0

We multiply all the terms by the denominator


2r*2r-8(-1r-5)+49*2r+49)-(+49)=0

We add all the numbers together, and all the variables

2r*2r-8(-1r-5)+49*2r+49)-49=0

We add all the numbers together, and all the variables

2r*2r-8(-1r-5)+49*2r=0

We multiply parentheses

2r*2r+8r+49*2r+40=0

Wy multiply elements

4r^2+8r+98r+40=0

We add all the numbers together, and all the variables

4r^2+106r+40=0

a = 4; b = 106; c = +40;
Δ = b2-4ac
Δ = 1062-4·4·40
Δ = 10596
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:

$\sqrt{\Delta}=\sqrt{10596}=\sqrt{4*2649}=\sqrt{4}*\sqrt{2649}=2\sqrt{2649}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(106)-2\sqrt{2649}}{2*4}=\frac{-106-2\sqrt{2649}}{8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(106)+2\sqrt{2649}}{2*4}=\frac{-106+2\sqrt{2649}}{8}
$