360/5x+18=x

Solution for 360/5x+18=x equation:

360/5x+18=x

We move all terms to the left:

360/5x+18-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+360/5x+18=0

We multiply all the terms by the denominator


-1x*5x+18*5x+360=0

Wy multiply elements

-5x^2+90x+360=0

a = -5; b = 90; c = +360;
Δ = b2-4ac
Δ = 902-4·(-5)·360
Δ = 15300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15300}=\sqrt{900*17}=\sqrt{900}*\sqrt{17}=30\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-30\sqrt{17}}{2*-5}=\frac{-90-30\sqrt{17}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+30\sqrt{17}}{2*-5}=\frac{-90+30\sqrt{17}}{-10}
$