49/25=r^2+2r+1

Solution for 49/25=r^2+2r+1 equation:

49/25=r^2+2r+1

We move all terms to the left:

49/25-(r^2+2r+1)=0

We get rid of parentheses

-r^2-2r-1+49/25=0

We multiply all the terms by the denominator


-r^2*25-2r*25+49-1*25=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-25r^2-50r+24=0

a = -25; b = -50; c = +24;
Δ = b2-4ac
Δ = -502-4·(-25)·24
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-70}{2*-25}=\frac{-20}{-50}
=2/5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+70}{2*-25}=\frac{120}{-50}
=-2+2/5
$