4x+10/x=14

Solution for 4x+10/x=14 equation:

4x+10/x=14

We move all terms to the left:

4x+10/x-(14)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


4x*x-14*x+10=0

We add all the numbers together, and all the variables

-14x+4x*x+10=0

Wy multiply elements

4x^2-14x+10=0

a = 4; b = -14; c = +10;
Δ = b2-4ac
Δ = -142-4·4·10
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6}{2*4}=\frac{20}{8}
=2+1/2
$