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

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

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

We move all terms to the left:

8r^2-(3r)=0

a = 8; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·8·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*8}=\frac{0}{16}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*8}=\frac{6}{16}
=3/8
$