15/45x-120=-24-12x

Solution for 15/45x-120=-24-12x equation:

15/45x-120=-24-12x

We move all terms to the left:

15/45x-120-(-24-12x)=0


Domain of the equation: 45x!=0

x!=0/45

x!=0

x∈R


We add all the numbers together, and all the variables

15/45x-(-12x-24)-120=0

We get rid of parentheses

15/45x+12x+24-120=0

We multiply all the terms by the denominator


12x*45x+24*45x-120*45x+15=0

Wy multiply elements

540x^2+1080x-5400x+15=0

We add all the numbers together, and all the variables

540x^2-4320x+15=0

a = 540; b = -4320; c = +15;
Δ = b2-4ac
Δ = -43202-4·540·15
Δ = 18630000
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:

$\sqrt{\Delta}=\sqrt{18630000}=\sqrt{810000*23}=\sqrt{810000}*\sqrt{23}=900\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4320)-900\sqrt{23}}{2*540}=\frac{4320-900\sqrt{23}}{1080}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4320)+900\sqrt{23}}{2*540}=\frac{4320+900\sqrt{23}}{1080}
$