(90/x)+3=12x=

Solution for (90/x)+3=12x= equation:

(90/x)+3=12x=

We move all terms to the left:

(90/x)+3-(12x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+90/x)-12x+3=0

We add all the numbers together, and all the variables

-12x+(+90/x)+3=0

We get rid of parentheses

-12x+90/x+3=0

We multiply all the terms by the denominator


-12x*x+3*x+90=0

We add all the numbers together, and all the variables

3x-12x*x+90=0

Wy multiply elements

-12x^2+3x+90=0

a = -12; b = 3; c = +90;
Δ = b2-4ac
Δ = 32-4·(-12)·90
Δ = 4329
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:

$\sqrt{\Delta}=\sqrt{4329}=\sqrt{9*481}=\sqrt{9}*\sqrt{481}=3\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{481}}{2*-12}=\frac{-3-3\sqrt{481}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{481}}{2*-12}=\frac{-3+3\sqrt{481}}{-24}
$