(3x-5)(7x-2)=0

Solution for (3x-5)(7x-2)=0 equation:

(3x-5)(7x-2)=0

We multiply parentheses ..

(+21x^2-6x-35x+10)=0

We get rid of parentheses

21x^2-6x-35x+10=0

We add all the numbers together, and all the variables

21x^2-41x+10=0

a = 21; b = -41; c = +10;
Δ = b2-4ac
Δ = -412-4·21·10
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-29}{2*21}=\frac{12}{42}
=2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+29}{2*21}=\frac{70}{42}
=1+2/3
$