(5x-21)(7x-3)=180

Solution for (5x-21)(7x-3)=180 equation:

(5x-21)(7x-3)=180

We move all terms to the left:

(5x-21)(7x-3)-(180)=0

We multiply parentheses ..

(+35x^2-15x-147x+63)-180=0

We get rid of parentheses

35x^2-15x-147x+63-180=0

We add all the numbers together, and all the variables

35x^2-162x-117=0

a = 35; b = -162; c = -117;
Δ = b2-4ac
Δ = -1622-4·35·(-117)
Δ = 42624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{42624}=\sqrt{576*74}=\sqrt{576}*\sqrt{74}=24\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-24\sqrt{74}}{2*35}=\frac{162-24\sqrt{74}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+24\sqrt{74}}{2*35}=\frac{162+24\sqrt{74}}{70}
$