5/7x+3/2x=1

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

5/7x+3/2x=1

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


10x/14x^2+21x/14x^2-1=0

We multiply all the terms by the denominator


10x+21x-1*14x^2=0

We add all the numbers together, and all the variables

31x-1*14x^2=0

Wy multiply elements

-14x^2+31x=0

a = -14; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-14)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-14}=\frac{-62}{-28}
=2+3/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-14}=\frac{0}{-28}
=0
$