-4/5x-12/5x+1/3x=-45

Solution for -4/5x-12/5x+1/3x=-45 equation:

-4/5x-12/5x+1/3x=-45

We move all terms to the left:

-4/5x-12/5x+1/3x-(-45)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-4/5x-12/5x+1/3x+45=0

We calculate fractions


(-36x-4)/15x^2+5x/15x^2+45=0

We multiply all the terms by the denominator


(-36x-4)+5x+45*15x^2=0

We add all the numbers together, and all the variables

5x+(-36x-4)+45*15x^2=0

Wy multiply elements

675x^2+5x+(-36x-4)=0

We get rid of parentheses

675x^2+5x-36x-4=0

We add all the numbers together, and all the variables

675x^2-31x-4=0

a = 675; b = -31; c = -4;
Δ = b2-4ac
Δ = -312-4·675·(-4)
Δ = 11761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{11761}}{2*675}=\frac{31-\sqrt{11761}}{1350}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{11761}}{2*675}=\frac{31+\sqrt{11761}}{1350}
$