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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+21x^2+15x-35x-25)-180=0

We get rid of parentheses

21x^2+15x-35x-25-180=0

We add all the numbers together, and all the variables

21x^2-20x-205=0

a = 21; b = -20; c = -205;
Δ = b2-4ac
Δ = -202-4·21·(-205)
Δ = 17620
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:

$\sqrt{\Delta}=\sqrt{17620}=\sqrt{4*4405}=\sqrt{4}*\sqrt{4405}=2\sqrt{4405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{4405}}{2*21}=\frac{20-2\sqrt{4405}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{4405}}{2*21}=\frac{20+2\sqrt{4405}}{42}
$