360/(x-4)=x+15

Solution for 360/(x-4)=x+15 equation:

360/(x-4)=x+15

We move all terms to the left:

360/(x-4)-(x+15)=0


Domain of the equation: (x-4)!=0

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

x!=4

x∈R


We get rid of parentheses

360/(x-4)-x-15=0

We multiply all the terms by the denominator


-x*(x-4)-15*(x-4)+360=0

We multiply parentheses

-x^2+4x-15x+60+360=0

We add all the numbers together, and all the variables

-1x^2-11x+420=0

a = -1; b = -11; c = +420;
Δ = b2-4ac
Δ = -112-4·(-1)·420
Δ = 1801
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{-(-11)-\sqrt{1801}}{2*-1}=\frac{11-\sqrt{1801}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{1801}}{2*-1}=\frac{11+\sqrt{1801}}{-2}
$