2x-(17/x+4)=7

Solution for 2x-(17/x+4)=7 equation:

2x-(17/x+4)=7

We move all terms to the left:

2x-(17/x+4)-(7)=0


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

x∈R


We get rid of parentheses

2x-17/x-4-7=0

We multiply all the terms by the denominator


2x*x-4*x-7*x-17=0

We add all the numbers together, and all the variables

-11x+2x*x-17=0

Wy multiply elements

2x^2-11x-17=0

a = 2; b = -11; c = -17;
Δ = b2-4ac
Δ = -112-4·2·(-17)
Δ = 257
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{-(-11)-\sqrt{257}}{2*2}=\frac{11-\sqrt{257}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{257}}{2*2}=\frac{11+\sqrt{257}}{4}
$