2r2+5=8r2-211

Solution for 2r2+5=8r2-211 equation:

2r^2+5=8r^2-211

We move all terms to the left:

2r^2+5-(8r^2-211)=0

We get rid of parentheses

2r^2-8r^2+211+5=0

We add all the numbers together, and all the variables

-6r^2+216=0

a = -6; b = 0; c = +216;
Δ = b2-4ac
Δ = 02-4·(-6)·216
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72}{2*-6}=\frac{-72}{-12}
=+6
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*-6}=\frac{72}{-12}
=-6
$