(2x-7/x+4)=3

Solution for (2x-7/x+4)=3 equation:

(2x-7/x+4)=3

We move all terms to the left:

(2x-7/x+4)-(3)=0


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x+2x*x-7=0

Wy multiply elements

2x^2+x-7=0

a = 2; b = 1; c = -7;
Δ = b2-4ac
Δ = 12-4·2·(-7)
Δ = 57
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{-(1)-\sqrt{57}}{2*2}=\frac{-1-\sqrt{57}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{57}}{2*2}=\frac{-1+\sqrt{57}}{4}
$