56/x2=4

Solution for 56/x2=4 equation:

56/x2=4

We move all terms to the left:

56/x2-(4)=0


Domain of the equation: x2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-4*x2+56=0

We add all the numbers together, and all the variables

-4x^2+56=0

a = -4; b = 0; c = +56;
Δ = b2-4ac
Δ = 02-4·(-4)·56
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*-4}=\frac{0-8\sqrt{14}}{-8}
=-\frac{8\sqrt{14}}{-8}
=-\frac{\sqrt{14}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*-4}=\frac{0+8\sqrt{14}}{-8}
=\frac{8\sqrt{14}}{-8}
=\frac{\sqrt{14}}{-1}
$