3/5*x+x+4(3/5*x)=2000

Solution for 3/5*x+x+4(3/5*x)=2000 equation:

3/5x+x+4(3/5x)=2000

We move all terms to the left:

3/5x+x+4(3/5x)-(2000)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x+x+4(+3/5x)-2000=0

We add all the numbers together, and all the variables

x+3/5x+4(+3/5x)-2000=0

We multiply parentheses

x+3/5x+12x-2000=0

We multiply all the terms by the denominator


x*5x+12x*5x-2000*5x+3=0

Wy multiply elements

5x^2+60x^2-10000x+3=0

We add all the numbers together, and all the variables

65x^2-10000x+3=0

a = 65; b = -10000; c = +3;
Δ = b2-4ac
Δ = -100002-4·65·3
Δ = 99999220
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{99999220}=\sqrt{4*24999805}=\sqrt{4}*\sqrt{24999805}=2\sqrt{24999805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10000)-2\sqrt{24999805}}{2*65}=\frac{10000-2\sqrt{24999805}}{130}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10000)+2\sqrt{24999805}}{2*65}=\frac{10000+2\sqrt{24999805}}{130}
$