(3x-5)(7x-2)=10

Solution for (3x-5)(7x-2)=10 equation:

(3x-5)(7x-2)=10

We move all terms to the left:

(3x-5)(7x-2)-(10)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

21x^2-41x=0

a = 21; b = -41; c = 0;
Δ = b2-4ac
Δ = -412-4·21·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-41}{2*21}=\frac{0}{42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+41}{2*21}=\frac{82}{42}
=1+20/21
$