1/4x+3=3/5x-18

Solution for 1/4x+3=3/5x-18 equation:

1/4x+3=3/5x-18

We move all terms to the left:

1/4x+3-(3/5x-18)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x-18)!=0

x∈R


We get rid of parentheses

1/4x-3/5x+18+3=0

We calculate fractions


5x/20x^2+(-12x)/20x^2+18+3=0

We add all the numbers together, and all the variables

5x/20x^2+(-12x)/20x^2+21=0

We multiply all the terms by the denominator


5x+(-12x)+21*20x^2=0

Wy multiply elements

420x^2+5x+(-12x)=0

We get rid of parentheses

420x^2+5x-12x=0

We add all the numbers together, and all the variables

420x^2-7x=0

a = 420; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·420·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*420}=\frac{0}{840}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*420}=\frac{14}{840}
=1/60
$