8^2+3r+2=7r^2

Solution for 8^2+3r+2=7r^2 equation:

8^2+3r+2=7r^2

We move all terms to the left:

8^2+3r+2-(7r^2)=0

determiningTheFunctionDomain
-7r^2+3r+2+8^2=0

We add all the numbers together, and all the variables

-7r^2+3r+66=0

a = -7; b = 3; c = +66;
Δ = b2-4ac
Δ = 32-4·(-7)·66
Δ = 1857
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{1857}}{2*-7}=\frac{-3-\sqrt{1857}}{-14}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{1857}}{2*-7}=\frac{-3+\sqrt{1857}}{-14}
$