144/x=108+3x

Solution for 144/x=108+3x equation:

144/x=108+3x

We move all terms to the left:

144/x-(108+3x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

144/x-(3x+108)=0

We get rid of parentheses

144/x-3x-108=0

We multiply all the terms by the denominator


-3x*x-108*x+144=0

We add all the numbers together, and all the variables

-108x-3x*x+144=0

Wy multiply elements

-3x^2-108x+144=0

a = -3; b = -108; c = +144;
Δ = b2-4ac
Δ = -1082-4·(-3)·144
Δ = 13392
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:

$\sqrt{\Delta}=\sqrt{13392}=\sqrt{144*93}=\sqrt{144}*\sqrt{93}=12\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-12\sqrt{93}}{2*-3}=\frac{108-12\sqrt{93}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+12\sqrt{93}}{2*-3}=\frac{108+12\sqrt{93}}{-6}
$