5x=5/2x+11

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

5x=5/2x+11

We move all terms to the left:

5x-(5/2x+11)=0


Domain of the equation: 2x+11)!=0

x∈R


We get rid of parentheses

5x-5/2x-11=0

We multiply all the terms by the denominator


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

Wy multiply elements

10x^2-22x-5=0

a = 10; b = -22; c = -5;
Δ = b2-4ac
Δ = -222-4·10·(-5)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-6\sqrt{19}}{2*10}=\frac{22-6\sqrt{19}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+6\sqrt{19}}{2*10}=\frac{22+6\sqrt{19}}{20}
$