-4x+3/x=-7

Solution for -4x+3/x=-7 equation:

-4x+3/x=-7

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-4x+3/x+7=0

We multiply all the terms by the denominator


-4x*x+7*x+3=0

We add all the numbers together, and all the variables

7x-4x*x+3=0

Wy multiply elements

-4x^2+7x+3=0

a = -4; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·(-4)·3
Δ = 97
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{-(7)-\sqrt{97}}{2*-4}=\frac{-7-\sqrt{97}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{97}}{2*-4}=\frac{-7+\sqrt{97}}{-8}
$