6.25=(1+r2)5

Solution for 6.25=(1+r2)5 equation:

6.25=(1+r2)5

We move all terms to the left:

6.25-((1+r2)5)=0

We add all the numbers together, and all the variables

-((+r^2+1)5)+6.25=0


We calculate terms in parentheses: -((+r^2+1)5), so:

(+r^2+1)5

We multiply parentheses

5r^2+5

Back to the equation:

-(5r^2+5)


We get rid of parentheses

-5r^2-5+6.25=0

We add all the numbers together, and all the variables

-5r^2+1.25=0

a = -5; b = 0; c = +1.25;
Δ = b2-4ac
Δ = 02-4·(-5)·1.25
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-5}{2*-5}=\frac{-5}{-10}
=1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+5}{2*-5}=\frac{5}{-10}
=-1/2
$