3(x+3)/15x-30x=12

Solution for 3(x+3)/15x-30x=12 equation:

3(x+3)/15x-30x=12

We move all terms to the left:

3(x+3)/15x-30x-(12)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We add all the numbers together, and all the variables

-30x+3(x+3)/15x-12=0

We multiply all the terms by the denominator


-30x*15x+3(x+3)-12*15x=0

We multiply parentheses

-30x*15x+3x-12*15x+9=0

Wy multiply elements

-450x^2+3x-180x+9=0

We add all the numbers together, and all the variables

-450x^2-177x+9=0

a = -450; b = -177; c = +9;
Δ = b2-4ac
Δ = -1772-4·(-450)·9
Δ = 47529
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:

$\sqrt{\Delta}=\sqrt{47529}=\sqrt{9*5281}=\sqrt{9}*\sqrt{5281}=3\sqrt{5281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-177)-3\sqrt{5281}}{2*-450}=\frac{177-3\sqrt{5281}}{-900}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-177)+3\sqrt{5281}}{2*-450}=\frac{177+3\sqrt{5281}}{-900}
$