(7x+3)(2x-3)=180

Solution for (7x+3)(2x-3)=180 equation:

(7x+3)(2x-3)=180

We move all terms to the left:

(7x+3)(2x-3)-(180)=0

We multiply parentheses ..

(+14x^2-21x+6x-9)-180=0

We get rid of parentheses

14x^2-21x+6x-9-180=0

We add all the numbers together, and all the variables

14x^2-15x-189=0

a = 14; b = -15; c = -189;
Δ = b2-4ac
Δ = -152-4·14·(-189)
Δ = 10809
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:

$\sqrt{\Delta}=\sqrt{10809}=\sqrt{9*1201}=\sqrt{9}*\sqrt{1201}=3\sqrt{1201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{1201}}{2*14}=\frac{15-3\sqrt{1201}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{1201}}{2*14}=\frac{15+3\sqrt{1201}}{28}
$