(3x-15)(7.5-x)=0

Solution for (3x-15)(7.5-x)=0 equation:

(3x-15)(7.5-x)=0

We add all the numbers together, and all the variables

(3x-15)(-1x+7.5)=0

We multiply parentheses ..

(-3x^2+22.5x+15x-112.5)=0

We get rid of parentheses

-3x^2+22.5x+15x-112.5=0

We add all the numbers together, and all the variables

-3x^2+37.5x-112.5=0

a = -3; b = 37.5; c = -112.5;
Δ = b2-4ac
Δ = 37.52-4·(-3)·(-112.5)
Δ = 56.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37.5)-\sqrt{56.25}}{2*-3}=\frac{-37.5-\sqrt{56.25}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37.5)+\sqrt{56.25}}{2*-3}=\frac{-37.5+\sqrt{56.25}}{-6}
$