15x-30=360/x

Solution for 15x-30=360/x equation:

15x-30=360/x

We move all terms to the left:

15x-30-(360/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

15x-(+360/x)-30=0

We get rid of parentheses

15x-360/x-30=0

We multiply all the terms by the denominator


15x*x-30*x-360=0

We add all the numbers together, and all the variables

-30x+15x*x-360=0

Wy multiply elements

15x^2-30x-360=0

a = 15; b = -30; c = -360;
Δ = b2-4ac
Δ = -302-4·15·(-360)
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-150}{2*15}=\frac{-120}{30}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+150}{2*15}=\frac{180}{30}
=6
$