r^2+r=24/25

Solution for r^2+r=24/25 equation:

r^2+r=24/25

We move all terms to the left:

r^2+r-(24/25)=0

We add all the numbers together, and all the variables

r^2+r-(+24/25)=0

We get rid of parentheses

r^2+r-24/25=0

We multiply all the terms by the denominator


r^2*25+r*25-24=0

Wy multiply elements

25r^2+25r-24=0

a = 25; b = 25; c = -24;
Δ = b2-4ac
Δ = 252-4·25·(-24)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-55}{2*25}=\frac{-80}{50}
=-1+3/5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+55}{2*25}=\frac{30}{50}
=3/5
$