102/x=20x-8

Solution for 102/x=20x-8 equation:

102/x=20x-8

We move all terms to the left:

102/x-(20x-8)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

102/x-20x+8=0

We multiply all the terms by the denominator


-20x*x+8*x+102=0

We add all the numbers together, and all the variables

8x-20x*x+102=0

Wy multiply elements

-20x^2+8x+102=0

a = -20; b = 8; c = +102;
Δ = b2-4ac
Δ = 82-4·(-20)·102
Δ = 8224
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:

$\sqrt{\Delta}=\sqrt{8224}=\sqrt{16*514}=\sqrt{16}*\sqrt{514}=4\sqrt{514}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{514}}{2*-20}=\frac{-8-4\sqrt{514}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{514}}{2*-20}=\frac{-8+4\sqrt{514}}{-40}
$