(7x-49)(3x-27)=0

Solution for (7x-49)(3x-27)=0 equation:

(7x-49)(3x-27)=0

We multiply parentheses ..

(+21x^2-189x-147x+1323)=0

We get rid of parentheses

21x^2-189x-147x+1323=0

We add all the numbers together, and all the variables

21x^2-336x+1323=0

a = 21; b = -336; c = +1323;
Δ = b2-4ac
Δ = -3362-4·21·1323
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-336)-42}{2*21}=\frac{294}{42}
=7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-336)+42}{2*21}=\frac{378}{42}
=9
$