2x-11/5x+11=0

Solution for 2x-11/5x+11=0 equation:

2x-11/5x+11=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


2x*5x+11*5x-11=0

Wy multiply elements

10x^2+55x-11=0

a = 10; b = 55; c = -11;
Δ = b2-4ac
Δ = 552-4·10·(-11)
Δ = 3465
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:

$\sqrt{\Delta}=\sqrt{3465}=\sqrt{9*385}=\sqrt{9}*\sqrt{385}=3\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-3\sqrt{385}}{2*10}=\frac{-55-3\sqrt{385}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+3\sqrt{385}}{2*10}=\frac{-55+3\sqrt{385}}{20}
$