15/x+19-12x=5

Solution for 15/x+19-12x=5 equation:

15/x+19-12x=5

We move all terms to the left:

15/x+19-12x-(5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-12x+15/x+14=0

We multiply all the terms by the denominator


-12x*x+14*x+15=0

We add all the numbers together, and all the variables

14x-12x*x+15=0

Wy multiply elements

-12x^2+14x+15=0

a = -12; b = 14; c = +15;
Δ = b2-4ac
Δ = 142-4·(-12)·15
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{229}}{2*-12}=\frac{-14-2\sqrt{229}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{229}}{2*-12}=\frac{-14+2\sqrt{229}}{-24}
$