3/4x+1/5x=8

Solution for 3/4x+1/5x=8 equation:

3/4x+1/5x=8

We move all terms to the left:

3/4x+1/5x-(8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


15x/20x^2+4x/20x^2-8=0

We multiply all the terms by the denominator


15x+4x-8*20x^2=0

We add all the numbers together, and all the variables

19x-8*20x^2=0

Wy multiply elements

-160x^2+19x=0

a = -160; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-160)·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*-160}=\frac{-38}{-320}
=19/160
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-160}=\frac{0}{-320}
=0
$