4x-10/x=3

Solution for 4x-10/x=3 equation:

4x-10/x=3

We move all terms to the left:

4x-10/x-(3)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


4x*x-3*x-10=0

We add all the numbers together, and all the variables

-3x+4x*x-10=0

Wy multiply elements

4x^2-3x-10=0

a = 4; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·4·(-10)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-13}{2*4}=\frac{-10}{8}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13}{2*4}=\frac{16}{8}
=2
$