7r^2-39r=-20

Solution for 7r^2-39r=-20 equation:

7r^2-39r=-20

We move all terms to the left:

7r^2-39r-(-20)=0

We add all the numbers together, and all the variables

7r^2-39r+20=0

a = 7; b = -39; c = +20;
Δ = b2-4ac
Δ = -392-4·7·20
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-31}{2*7}=\frac{8}{14}
=4/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+31}{2*7}=\frac{70}{14}
=5
$