1/5x+15x=40

Solution for 1/5x+15x=40 equation:

1/5x+15x=40

We move all terms to the left:

1/5x+15x-(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

15x+1/5x-40=0

We multiply all the terms by the denominator


15x*5x-40*5x+1=0

Wy multiply elements

75x^2-200x+1=0

a = 75; b = -200; c = +1;
Δ = b2-4ac
Δ = -2002-4·75·1
Δ = 39700
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:

$\sqrt{\Delta}=\sqrt{39700}=\sqrt{100*397}=\sqrt{100}*\sqrt{397}=10\sqrt{397}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-10\sqrt{397}}{2*75}=\frac{200-10\sqrt{397}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+10\sqrt{397}}{2*75}=\frac{200+10\sqrt{397}}{150}
$