8500=7265(1+r(2))

Solution for 8500=7265(1+r(2)) equation:

8500=7265(1+r(2))

We move all terms to the left:

8500-(7265(1+r(2)))=0

We add all the numbers together, and all the variables

-(7265(+r^2+1))+8500=0


We calculate terms in parentheses: -(7265(+r^2+1)), so:

7265(+r^2+1)

We multiply parentheses

7265r^2+7265

Back to the equation:

-(7265r^2+7265)


We get rid of parentheses

-7265r^2-7265+8500=0

We add all the numbers together, and all the variables

-7265r^2+1235=0

a = -7265; b = 0; c = +1235;
Δ = b2-4ac
Δ = 02-4·(-7265)·1235
Δ = 35889100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{35889100}=\sqrt{100*358891}=\sqrt{100}*\sqrt{358891}=10\sqrt{358891}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{358891}}{2*-7265}=\frac{0-10\sqrt{358891}}{-14530}
=-\frac{10\sqrt{358891}}{-14530}
=-\frac{\sqrt{358891}}{-1453}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{358891}}{2*-7265}=\frac{0+10\sqrt{358891}}{-14530}
=\frac{10\sqrt{358891}}{-14530}
=\frac{\sqrt{358891}}{-1453}
$