15/x-4x=-7

Solution for 15/x-4x=-7 equation:

15/x-4x=-7

We move all terms to the left:

15/x-4x-(-7)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-4x+15/x+7=0

We multiply all the terms by the denominator


-4x*x+7*x+15=0

We add all the numbers together, and all the variables

7x-4x*x+15=0

Wy multiply elements

-4x^2+7x+15=0

a = -4; b = 7; c = +15;
Δ = b2-4ac
Δ = 72-4·(-4)·15
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*-4}=\frac{-24}{-8}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*-4}=\frac{10}{-8}
=-1+1/4
$