(3x-7)(7x-2)=0

Solution for (3x-7)(7x-2)=0 equation:

(3x-7)(7x-2)=0

We multiply parentheses ..

(+21x^2-6x-49x+14)=0

We get rid of parentheses

21x^2-6x-49x+14=0

We add all the numbers together, and all the variables

21x^2-55x+14=0

a = 21; b = -55; c = +14;
Δ = b2-4ac
Δ = -552-4·21·14
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-43}{2*21}=\frac{12}{42}
=2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+43}{2*21}=\frac{98}{42}
=2+1/3
$