5/7x-3=1/2x+9

Solution for 5/7x-3=1/2x+9 equation:

5/7x-3=1/2x+9

We move all terms to the left:

5/7x-3-(1/2x+9)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x+9)!=0

x∈R


We get rid of parentheses

5/7x-1/2x-9-3=0

We calculate fractions


10x/14x^2+(-7x)/14x^2-9-3=0

We add all the numbers together, and all the variables

10x/14x^2+(-7x)/14x^2-12=0

We multiply all the terms by the denominator


10x+(-7x)-12*14x^2=0

Wy multiply elements

-168x^2+10x+(-7x)=0

We get rid of parentheses

-168x^2+10x-7x=0

We add all the numbers together, and all the variables

-168x^2+3x=0

a = -168; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-168)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-168}=\frac{-6}{-336}
=1/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-168}=\frac{0}{-336}
=0
$