3/5x+x=40

Solution for 3/5x+x=40 equation:

3/5x+x=40

We move all terms to the left:

3/5x+x-(40)=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-40=0

We multiply all the terms by the denominator


x*5x-40*5x+3=0

Wy multiply elements

5x^2-200x+3=0

a = 5; b = -200; c = +3;
Δ = b2-4ac
Δ = -2002-4·5·3
Δ = 39940
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:

$\sqrt{\Delta}=\sqrt{39940}=\sqrt{4*9985}=\sqrt{4}*\sqrt{9985}=2\sqrt{9985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-2\sqrt{9985}}{2*5}=\frac{200-2\sqrt{9985}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+2\sqrt{9985}}{2*5}=\frac{200+2\sqrt{9985}}{10}
$