x-56/2=3/x

Solution for x-56/2=3/x equation:

x-56/2=3/x

We move all terms to the left:

x-56/2-(3/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+3/x)-56/2=0

We add all the numbers together, and all the variables

x-(+3/x)-28=0

We get rid of parentheses

x-3/x-28=0

We multiply all the terms by the denominator


x*x-28*x-3=0

We add all the numbers together, and all the variables

-28x+x*x-3=0

Wy multiply elements

x^2-28x-3=0

a = 1; b = -28; c = -3;
Δ = b2-4ac
Δ = -282-4·1·(-3)
Δ = 796
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{796}=\sqrt{4*199}=\sqrt{4}*\sqrt{199}=2\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{199}}{2*1}=\frac{28-2\sqrt{199}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{199}}{2*1}=\frac{28+2\sqrt{199}}{2}
$