3/5x+14=7/20x-4

Solution for 3/5x+14=7/20x-4 equation:

3/5x+14=7/20x-4

We move all terms to the left:

3/5x+14-(7/20x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 20x-4)!=0

x∈R


We get rid of parentheses

3/5x-7/20x+4+14=0

We calculate fractions


60x/100x^2+(-35x)/100x^2+4+14=0

We add all the numbers together, and all the variables

60x/100x^2+(-35x)/100x^2+18=0

We multiply all the terms by the denominator


60x+(-35x)+18*100x^2=0

Wy multiply elements

1800x^2+60x+(-35x)=0

We get rid of parentheses

1800x^2+60x-35x=0

We add all the numbers together, and all the variables

1800x^2+25x=0

a = 1800; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·1800·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*1800}=\frac{-50}{3600}
=-1/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*1800}=\frac{0}{3600}
=0
$