25+r=-5(2+8r)/6r

Solution for 25+r=-5(2+8r)/6r equation:

25+r=-5(2+8r)/6r

We move all terms to the left:

25+r-(-5(2+8r)/6r)=0


Domain of the equation: 6r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

r-(-5(8r+2)/6r)+25=0

We multiply all the terms by the denominator


r*6r)-(-5(8r+2)+25*6r)=0

We multiply parentheses

r*6r)-(-40r+25*6r)-10=0

Wy multiply elements

6r^2-40r+150r=0

We add all the numbers together, and all the variables

6r^2+110r=0

a = 6; b = 110; c = 0;
Δ = b2-4ac
Δ = 1102-4·6·0
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-110}{2*6}=\frac{-220}{12}
=-18+1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+110}{2*6}=\frac{0}{12}
=0
$