3/5x-4=8+3/20x

Solution for 3/5x-4=8+3/20x equation:

3/5x-4=8+3/20x

We move all terms to the left:

3/5x-4-(8+3/20x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 20x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(3/20x+8)-4=0

We get rid of parentheses

3/5x-3/20x-8-4=0

We calculate fractions


60x/100x^2+(-15x)/100x^2-8-4=0

We add all the numbers together, and all the variables

60x/100x^2+(-15x)/100x^2-12=0

We multiply all the terms by the denominator


60x+(-15x)-12*100x^2=0

Wy multiply elements

-1200x^2+60x+(-15x)=0

We get rid of parentheses

-1200x^2+60x-15x=0

We add all the numbers together, and all the variables

-1200x^2+45x=0

a = -1200; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-1200)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-1200}=\frac{-90}{-2400}
=3/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-1200}=\frac{0}{-2400}
=0
$