5+2/x+5/4x=73/12

Solution for 5+2/x+5/4x=73/12 equation:

5+2/x+5/4x=73/12

We move all terms to the left:

5+2/x+5/4x-(73/12)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2/x+5/4x+5-(+73/12)=0

We get rid of parentheses

2/x+5/4x+5-73/12=0

We calculate fractions


(-1168x^2)/48x^2+96x/48x^2+60x/48x^2+5=0

We multiply all the terms by the denominator


(-1168x^2)+96x+60x+5*48x^2=0

We add all the numbers together, and all the variables

(-1168x^2)+156x+5*48x^2=0

Wy multiply elements

(-1168x^2)+240x^2+156x=0

We get rid of parentheses

-1168x^2+240x^2+156x=0

We add all the numbers together, and all the variables

-928x^2+156x=0

a = -928; b = 156; c = 0;
Δ = b2-4ac
Δ = 1562-4·(-928)·0
Δ = 24336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24336}=156$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-156}{2*-928}=\frac{-312}{-1856}
=39/232
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+156}{2*-928}=\frac{0}{-1856}
=0
$