4x-10=9/x

Solution for 4x-10=9/x equation:

4x-10=9/x

We move all terms to the left:

4x-10-(9/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+9/x)-10=0

We get rid of parentheses

4x-9/x-10=0

We multiply all the terms by the denominator


4x*x-10*x-9=0

We add all the numbers together, and all the variables

-10x+4x*x-9=0

Wy multiply elements

4x^2-10x-9=0

a = 4; b = -10; c = -9;
Δ = b2-4ac
Δ = -102-4·4·(-9)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{61}}{2*4}=\frac{10-2\sqrt{61}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{61}}{2*4}=\frac{10+2\sqrt{61}}{8}
$