7(r-3)(r+7)=0

Solution for 7(r-3)(r+7)=0 equation:

7(r-3)(r+7)=0

We multiply parentheses ..

7(+r^2+7r-3r-21)=0

We multiply parentheses

7r^2+49r-21r-147=0

We add all the numbers together, and all the variables

7r^2+28r-147=0

a = 7; b = 28; c = -147;
Δ = b2-4ac
Δ = 282-4·7·(-147)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-70}{2*7}=\frac{-98}{14}
=-7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+70}{2*7}=\frac{42}{14}
=3
$