1/4x+3=-183/5x

Solution for 1/4x+3=-183/5x equation:

1/4x+3=-183/5x

We move all terms to the left:

1/4x+3-(-183/5x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

1/4x+183/5x+3=0

We calculate fractions


5x/20x^2+732x/20x^2+3=0

We multiply all the terms by the denominator


5x+732x+3*20x^2=0

We add all the numbers together, and all the variables

737x+3*20x^2=0

Wy multiply elements

60x^2+737x=0

a = 60; b = 737; c = 0;
Δ = b2-4ac
Δ = 7372-4·60·0
Δ = 543169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{543169}=737$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(737)-737}{2*60}=\frac{-1474}{120}
=-12+17/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(737)+737}{2*60}=\frac{0}{120}
=0
$