120/x=4;x=5

Solution for 120/x=4;x=5 equation:

120/x=4x=5

We move all terms to the left:

120/x-(4x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-4x+120/x=0

We multiply all the terms by the denominator


-4x*x+120=0

Wy multiply elements

-4x^2+120=0

a = -4; b = 0; c = +120;
Δ = b2-4ac
Δ = 02-4·(-4)·120
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{30}}{2*-4}=\frac{0-8\sqrt{30}}{-8}
=-\frac{8\sqrt{30}}{-8}
=-\frac{\sqrt{30}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{30}}{2*-4}=\frac{0+8\sqrt{30}}{-8}
=\frac{8\sqrt{30}}{-8}
=\frac{\sqrt{30}}{-1}
$