2x=7/x-4=-1

Solution for 2x=7/x-4=-1 equation:

2x=7/x-4=-1

We move all terms to the left:

2x-(7/x-4)=0


Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

2x-7/x+4=0

We multiply all the terms by the denominator


2x*x+4*x-7=0

We add all the numbers together, and all the variables

4x+2x*x-7=0

Wy multiply elements

2x^2+4x-7=0

a = 2; b = 4; c = -7;
Δ = b2-4ac
Δ = 42-4·2·(-7)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{2}}{2*2}=\frac{-4-6\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{2}}{2*2}=\frac{-4+6\sqrt{2}}{4}
$