40=1/5x+3x=6

Solution for 40=1/5x+3x=6 equation:

40=1/5x+3x=6

We move all terms to the left:

40-(1/5x+3x)=0


Domain of the equation: 5x+3x)!=0

x∈R


We add all the numbers together, and all the variables

-(+3x+1/5x)+40=0

We get rid of parentheses

-3x-1/5x+40=0

We multiply all the terms by the denominator


-3x*5x+40*5x-1=0

Wy multiply elements

-15x^2+200x-1=0

a = -15; b = 200; c = -1;
Δ = b2-4ac
Δ = 2002-4·(-15)·(-1)
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*-15}=\frac{-200-2\sqrt{9985}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+2\sqrt{9985}}{2*-15}=\frac{-200+2\sqrt{9985}}{-30}
$