10x+10+360/X=20X+10

Solution for 10x+10+360/X=20X+10 equation:

10x+10+360/x=20x+10

We move all terms to the left:

10x+10+360/x-(20x+10)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

10x+360/x-20x-10+10=0

We multiply all the terms by the denominator


10x*x-20x*x-10*x+10*x+360=0

We add all the numbers together, and all the variables

10x*x-20x*x+360=0

Wy multiply elements

10x^2-20x^2+360=0

We add all the numbers together, and all the variables

-10x^2+360=0

a = -10; b = 0; c = +360;
Δ = b2-4ac
Δ = 02-4·(-10)·360
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120}{2*-10}=\frac{-120}{-20}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120}{2*-10}=\frac{120}{-20}
=-6
$