18/x-4=10x

Solution for 18/x-4=10x equation:

18/x-4=10x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-10x+18/x-4=0

We multiply all the terms by the denominator


-10x*x-4*x+18=0

We add all the numbers together, and all the variables

-4x-10x*x+18=0

Wy multiply elements

-10x^2-4x+18=0

a = -10; b = -4; c = +18;
Δ = b2-4ac
Δ = -42-4·(-10)·18
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{46}}{2*-10}=\frac{4-4\sqrt{46}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{46}}{2*-10}=\frac{4+4\sqrt{46}}{-20}
$