6.25r^2-100=r^2-4

Solution for 6.25r^2-100=r^2-4 equation:

6.25r^2-100=r^2-4

We move all terms to the left:

6.25r^2-100-(r^2-4)=0

We get rid of parentheses

6.25r^2-r^2+4-100=0

We add all the numbers together, and all the variables

5.25r^2-96=0

a = 5.25; b = 0; c = -96;
Δ = b2-4ac
Δ = 02-4·5.25·(-96)
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{14}}{2*5.25}=\frac{0-12\sqrt{14}}{10.5}
=-\frac{12\sqrt{14}}{10.5}
=-\frac{6\sqrt{14}}{5.25}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{14}}{2*5.25}=\frac{0+12\sqrt{14}}{10.5}
=\frac{12\sqrt{14}}{10.5}
=\frac{6\sqrt{14}}{5.25}
$