r+8.8=3r+7/r=0.1

Solution for r+8.8=3r+7/r=0.1 equation:

r+8.8=3r+7/r=0.1

We move all terms to the left:

r+8.8-(3r+7/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

r-(+3r+7/r)+8.8=0

We get rid of parentheses

r-3r-7/r+8.8=0

We multiply all the terms by the denominator


r*r-3r*r+(8.8)*r-7=0

We multiply parentheses

r*r-3r*r+8.8r-7=0

Wy multiply elements

r^2-3r^2+8.8r-7=0

We add all the numbers together, and all the variables

-2r^2+8.8r-7=0

a = -2; b = 8.8; c = -7;
Δ = b2-4ac
Δ = 8.82-4·(-2)·(-7)
Δ = 21.44
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{-(8.8)-\sqrt{21.44}}{2*-2}=\frac{-8.8-\sqrt{21.44}}{-4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8.8)+\sqrt{21.44}}{2*-2}=\frac{-8.8+\sqrt{21.44}}{-4}
$