5/60.2r+0.75=0.5r

Solution for 5/60.2r+0.75=0.5r equation:

5/60.2r+0.75=0.5r

We move all terms to the left:

5/60.2r+0.75-(0.5r)=0


Domain of the equation: 60.2r!=0

r!=0/60.2

r!=0

r∈R


We add all the numbers together, and all the variables

5/60.2r-(+0.5r)+0.75=0

We get rid of parentheses

5/60.2r-0.5r+0.75=0

We multiply all the terms by the denominator


-(0.5r)*60.2r+(0.75)*60.2r+5=0

We add all the numbers together, and all the variables

-(+0.5r)*60.2r+(0.75)*60.2r+5=0

We multiply parentheses

-0r^2+45r+5=0

We add all the numbers together, and all the variables

-1r^2+45r+5=0

a = -1; b = 45; c = +5;
Δ = b2-4ac
Δ = 452-4·(-1)·5
Δ = 2045
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{-(45)-\sqrt{2045}}{2*-1}=\frac{-45-\sqrt{2045}}{-2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2045}}{2*-1}=\frac{-45+\sqrt{2045}}{-2}
$