5x-11=1/2x+16

Solution for 5x-11=1/2x+16 equation:

5x-11=1/2x+16

We move all terms to the left:

5x-11-(1/2x+16)=0


Domain of the equation: 2x+16)!=0

x∈R


We get rid of parentheses

5x-1/2x-16-11=0

We multiply all the terms by the denominator


5x*2x-16*2x-11*2x-1=0

Wy multiply elements

10x^2-32x-22x-1=0

We add all the numbers together, and all the variables

10x^2-54x-1=0

a = 10; b = -54; c = -1;
Δ = b2-4ac
Δ = -542-4·10·(-1)
Δ = 2956
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:

$\sqrt{\Delta}=\sqrt{2956}=\sqrt{4*739}=\sqrt{4}*\sqrt{739}=2\sqrt{739}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{739}}{2*10}=\frac{54-2\sqrt{739}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{739}}{2*10}=\frac{54+2\sqrt{739}}{20}
$