(-x^2+15x)/(x-5)=0

Solution for (-x^2+15x)/(x-5)=0 equation:

(-x^2+15x)/(x-5)=0


Domain of the equation: (x-5)!=0

We move all terms containing x to the left, all other terms to the right

x!=5

x∈R


We multiply all the terms by the denominator


(-x^2+15x)=0

We get rid of parentheses

-x^2+15x=0

We add all the numbers together, and all the variables

-1x^2+15x=0

a = -1; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-1)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-1}=\frac{-30}{-2}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-1}=\frac{0}{-2}
=0
$