(x+21)(3x-7)=0

Solution for (x+21)(3x-7)=0 equation:

(x+21)(3x-7)=0

We multiply parentheses ..

(+3x^2-7x+63x-147)=0

We get rid of parentheses

3x^2-7x+63x-147=0

We add all the numbers together, and all the variables

3x^2+56x-147=0

a = 3; b = 56; c = -147;
Δ = b2-4ac
Δ = 562-4·3·(-147)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-70}{2*3}=\frac{-126}{6}
=-21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+70}{2*3}=\frac{14}{6}
=2+1/3
$