3x+75/x=36

Solution for 3x+75/x=36 equation:

3x+75/x=36

We move all terms to the left:

3x+75/x-(36)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


3x*x-36*x+75=0

We add all the numbers together, and all the variables

-36x+3x*x+75=0

Wy multiply elements

3x^2-36x+75=0

a = 3; b = -36; c = +75;
Δ = b2-4ac
Δ = -362-4·3·75
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{11}}{2*3}=\frac{36-6\sqrt{11}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{11}}{2*3}=\frac{36+6\sqrt{11}}{6}
$