1/2x+5/7x=3

Solution for 1/2x+5/7x=3 equation:

1/2x+5/7x=3

We move all terms to the left:

1/2x+5/7x-(3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We calculate fractions


7x/14x^2+10x/14x^2-3=0

We multiply all the terms by the denominator


7x+10x-3*14x^2=0

We add all the numbers together, and all the variables

17x-3*14x^2=0

Wy multiply elements

-42x^2+17x=0

a = -42; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-42)·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*-42}=\frac{-34}{-84}
=17/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-42}=\frac{0}{-84}
=0
$