14r^2=13r-3

Solution for 14r^2=13r-3 equation:

14r^2=13r-3

We move all terms to the left:

14r^2-(13r-3)=0

We get rid of parentheses

14r^2-13r+3=0

a = 14; b = -13; c = +3;
Δ = b2-4ac
Δ = -132-4·14·3
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-1}{2*14}=\frac{12}{28}
=3/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+1}{2*14}=\frac{14}{28}
=1/2
$