1/5x+3/4x=6

Solution for 1/5x+3/4x=6 equation:

1/5x+3/4x=6

We move all terms to the left:

1/5x+3/4x-(6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


4x/20x^2+15x/20x^2-6=0

We multiply all the terms by the denominator


4x+15x-6*20x^2=0

We add all the numbers together, and all the variables

19x-6*20x^2=0

Wy multiply elements

-120x^2+19x=0

a = -120; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-120)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-120}=\frac{-38}{-240}
=19/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-120}=\frac{0}{-240}
=0
$