(3x-21)(7x-42)=0

Solution for (3x-21)(7x-42)=0 equation:

(3x-21)(7x-42)=0

We multiply parentheses ..

(+21x^2-126x-147x+882)=0

We get rid of parentheses

21x^2-126x-147x+882=0

We add all the numbers together, and all the variables

21x^2-273x+882=0

a = 21; b = -273; c = +882;
Δ = b2-4ac
Δ = -2732-4·21·882
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-273)-21}{2*21}=\frac{252}{42}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-273)+21}{2*21}=\frac{294}{42}
=7
$