3/5x+1/2x=4

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

3/5x+1/2x=4

We move all terms to the left:

3/5x+1/2x-(4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


6x/10x^2+5x/10x^2-4=0

We multiply all the terms by the denominator


6x+5x-4*10x^2=0

We add all the numbers together, and all the variables

11x-4*10x^2=0

Wy multiply elements

-40x^2+11x=0

a = -40; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-40)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-40}=\frac{-22}{-80}
=11/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-40}=\frac{0}{-80}
=0
$