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

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

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

We multiply parentheses ..

7(+3x^2-7x+9x-21)=0

We multiply parentheses

21x^2-49x+63x-147=0

We add all the numbers together, and all the variables

21x^2+14x-147=0

a = 21; b = 14; c = -147;
Δ = b2-4ac
Δ = 142-4·21·(-147)
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-112}{2*21}=\frac{-126}{42}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+112}{2*21}=\frac{98}{42}
=2+1/3
$