5x+11=1/27x+28

Solution for 5x+11=1/27x+28 equation:

5x+11=1/27x+28

We move all terms to the left:

5x+11-(1/27x+28)=0


Domain of the equation: 27x+28)!=0

x∈R


We get rid of parentheses

5x-1/27x-28+11=0

We multiply all the terms by the denominator


5x*27x-28*27x+11*27x-1=0

Wy multiply elements

135x^2-756x+297x-1=0

We add all the numbers together, and all the variables

135x^2-459x-1=0

a = 135; b = -459; c = -1;
Δ = b2-4ac
Δ = -4592-4·135·(-1)
Δ = 211221
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:

$\sqrt{\Delta}=\sqrt{211221}=\sqrt{9*23469}=\sqrt{9}*\sqrt{23469}=3\sqrt{23469}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-459)-3\sqrt{23469}}{2*135}=\frac{459-3\sqrt{23469}}{270}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-459)+3\sqrt{23469}}{2*135}=\frac{459+3\sqrt{23469}}{270}
$