3/5x+1/4x=8*1/2

Solution for 3/5x+1/4x=8*1/2 equation:

3/5x+1/4x=8*1/2

We move all terms to the left:

3/5x+1/4x-(8*1/2)=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 add all the numbers together, and all the variables

3/5x+1/4x-4=0

We calculate fractions


12x/20x^2+5x/20x^2-4=0

We multiply all the terms by the denominator


12x+5x-4*20x^2=0

We add all the numbers together, and all the variables

17x-4*20x^2=0

Wy multiply elements

-80x^2+17x=0

a = -80; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-80)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-80}=\frac{-34}{-160}
=17/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-80}=\frac{0}{-160}
=0
$