(3x+5)(x-25)=180

Solution for (3x+5)(x-25)=180 equation:

(3x+5)(x-25)=180

We move all terms to the left:

(3x+5)(x-25)-(180)=0

We multiply parentheses ..

(+3x^2-75x+5x-125)-180=0

We get rid of parentheses

3x^2-75x+5x-125-180=0

We add all the numbers together, and all the variables

3x^2-70x-305=0

a = 3; b = -70; c = -305;
Δ = b2-4ac
Δ = -702-4·3·(-305)
Δ = 8560
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:

$\sqrt{\Delta}=\sqrt{8560}=\sqrt{16*535}=\sqrt{16}*\sqrt{535}=4\sqrt{535}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-4\sqrt{535}}{2*3}=\frac{70-4\sqrt{535}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+4\sqrt{535}}{2*3}=\frac{70+4\sqrt{535}}{6}
$