2/x=x/5x-12

Solution for 2/x=x/5x-12 equation:

2/x=x/5x-12

We move all terms to the left:

2/x-(x/5x-12)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x-12)!=0

x∈R


We get rid of parentheses

2/x-x/5x+12=0

We calculate fractions


(-1x^2)/5x^2+10x/5x^2+12=0

We multiply all the terms by the denominator


(-1x^2)+10x+12*5x^2=0

Wy multiply elements

(-1x^2)+60x^2+10x=0

We get rid of parentheses

-1x^2+60x^2+10x=0

We add all the numbers together, and all the variables

59x^2+10x=0

a = 59; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·59·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*59}=\frac{-20}{118}
=-10/59
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*59}=\frac{0}{118}
=0
$