(3x-5)(7x+2)=9

Solution for (3x-5)(7x+2)=9 equation:

(3x-5)(7x+2)=9

We move all terms to the left:

(3x-5)(7x+2)-(9)=0

We multiply parentheses ..

(+21x^2+6x-35x-10)-9=0

We get rid of parentheses

21x^2+6x-35x-10-9=0

We add all the numbers together, and all the variables

21x^2-29x-19=0

a = 21; b = -29; c = -19;
Δ = b2-4ac
Δ = -292-4·21·(-19)
Δ = 2437
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-\sqrt{2437}}{2*21}=\frac{29-\sqrt{2437}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{2437}}{2*21}=\frac{29+\sqrt{2437}}{42}
$