4x+6/x=25

Solution for 4x+6/x=25 equation:

4x+6/x=25

We move all terms to the left:

4x+6/x-(25)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


4x*x-25*x+6=0

We add all the numbers together, and all the variables

-25x+4x*x+6=0

Wy multiply elements

4x^2-25x+6=0

a = 4; b = -25; c = +6;
Δ = b2-4ac
Δ = -252-4·4·6
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-23}{2*4}=\frac{2}{8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+23}{2*4}=\frac{48}{8}
=6
$