3(4x-7)=10/x

Solution for 3(4x-7)=10/x equation:

3(4x-7)=10/x

We move all terms to the left:

3(4x-7)-(10/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

3(4x-7)-(+10/x)=0

We multiply parentheses

12x-(+10/x)-21=0

We get rid of parentheses

12x-10/x-21=0

We multiply all the terms by the denominator


12x*x-21*x-10=0

We add all the numbers together, and all the variables

-21x+12x*x-10=0

Wy multiply elements

12x^2-21x-10=0

a = 12; b = -21; c = -10;
Δ = b2-4ac
Δ = -212-4·12·(-10)
Δ = 921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{921}}{2*12}=\frac{21-\sqrt{921}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{921}}{2*12}=\frac{21+\sqrt{921}}{24}
$