360/10x=x-5

Solution for 360/10x=x-5 equation:

360/10x=x-5

We move all terms to the left:

360/10x-(x-5)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

360/10x-x+5=0

We multiply all the terms by the denominator


-x*10x+5*10x+360=0

Wy multiply elements

-10x^2+50x+360=0

a = -10; b = 50; c = +360;
Δ = b2-4ac
Δ = 502-4·(-10)·360
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-130}{2*-10}=\frac{-180}{-20}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+130}{2*-10}=\frac{80}{-20}
=-4
$