(2x-3)*(15-x)=0

Solution for (2x-3)*(15-x)=0 equation:

(2x-3)(15-x)=0

We add all the numbers together, and all the variables

(2x-3)(-1x+15)=0

We multiply parentheses ..

(-2x^2+30x+3x-45)=0

We get rid of parentheses

-2x^2+30x+3x-45=0

We add all the numbers together, and all the variables

-2x^2+33x-45=0

a = -2; b = 33; c = -45;
Δ = b2-4ac
Δ = 332-4·(-2)·(-45)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-27}{2*-2}=\frac{-60}{-4}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+27}{2*-2}=\frac{-6}{-4}
=1+1/2
$