5/2x-5/6x=43

Solution for 5/2x-5/6x=43 equation:

5/2x-5/6x=43

We move all terms to the left:

5/2x-5/6x-(43)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


30x/12x^2+(-10x)/12x^2-43=0

We multiply all the terms by the denominator


30x+(-10x)-43*12x^2=0

Wy multiply elements

-516x^2+30x+(-10x)=0

We get rid of parentheses

-516x^2+30x-10x=0

We add all the numbers together, and all the variables

-516x^2+20x=0

a = -516; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-516)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-516}=\frac{-40}{-1032}
=5/129
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-516}=\frac{0}{-1032}
=0
$