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

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

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

We multiply parentheses ..

(+14x^2-6x-21x+9)=0

We get rid of parentheses

14x^2-6x-21x+9=0

We add all the numbers together, and all the variables

14x^2-27x+9=0

a = 14; b = -27; c = +9;
Δ = b2-4ac
Δ = -272-4·14·9
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-15}{2*14}=\frac{12}{28}
=3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+15}{2*14}=\frac{42}{28}
=1+1/2
$