24-1/3(4x)=18-1/30(3x)

Solution for 24-1/3(4x)=18-1/30(3x) equation:

24-1/3(4x)=18-1/30(3x)

We move all terms to the left:

24-1/3(4x)-(18-1/30(3x))=0


Domain of the equation: 34x!=0

x!=0/34

x!=0

x∈R



Domain of the equation: 303x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/34x-(-1/303x+18)+24=0

We get rid of parentheses

-1/34x+1/303x-18+24=0

We calculate fractions


(-303x)/10302x^2+34x/10302x^2-18+24=0

We add all the numbers together, and all the variables

(-303x)/10302x^2+34x/10302x^2+6=0

We multiply all the terms by the denominator


(-303x)+34x+6*10302x^2=0

We add all the numbers together, and all the variables

34x+(-303x)+6*10302x^2=0

Wy multiply elements

61812x^2+34x+(-303x)=0

We get rid of parentheses

61812x^2+34x-303x=0

We add all the numbers together, and all the variables

61812x^2-269x=0

a = 61812; b = -269; c = 0;
Δ = b2-4ac
Δ = -2692-4·61812·0
Δ = 72361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{72361}=269$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-269)-269}{2*61812}=\frac{0}{123624}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-269)+269}{2*61812}=\frac{538}{123624}
=269/61812
$