5x+1=11/2x+16

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

5x+1=11/2x+16

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

10x^2-32x+2x-11=0

We add all the numbers together, and all the variables

10x^2-30x-11=0

a = 10; b = -30; c = -11;
Δ = b2-4ac
Δ = -302-4·10·(-11)
Δ = 1340
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:

$\sqrt{\Delta}=\sqrt{1340}=\sqrt{4*335}=\sqrt{4}*\sqrt{335}=2\sqrt{335}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{335}}{2*10}=\frac{30-2\sqrt{335}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{335}}{2*10}=\frac{30+2\sqrt{335}}{20}
$