3/5x+x=600

Solution for 3/5x+x=600 equation:

3/5x+x=600

We move all terms to the left:

3/5x+x-(600)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/5x-600=0

We multiply all the terms by the denominator


x*5x-600*5x+3=0

Wy multiply elements

5x^2-3000x+3=0

a = 5; b = -3000; c = +3;
Δ = b2-4ac
Δ = -30002-4·5·3
Δ = 8999940
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:

$\sqrt{\Delta}=\sqrt{8999940}=\sqrt{4*2249985}=\sqrt{4}*\sqrt{2249985}=2\sqrt{2249985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3000)-2\sqrt{2249985}}{2*5}=\frac{3000-2\sqrt{2249985}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3000)+2\sqrt{2249985}}{2*5}=\frac{3000+2\sqrt{2249985}}{10}
$