11x-33/14x+159.5=220

Solution for 11x-33/14x+159.5=220 equation:

11x-33/14x+159.5=220

We move all terms to the left:

11x-33/14x+159.5-(220)=0


Domain of the equation: 14x!=0

x!=0/14

x!=0

x∈R


We add all the numbers together, and all the variables

11x-33/14x-60.5=0

We multiply all the terms by the denominator


11x*14x-(60.5)*14x-33=0

We multiply parentheses

11x*14x-847x-33=0

Wy multiply elements

154x^2-847x-33=0

a = 154; b = -847; c = -33;
Δ = b2-4ac
Δ = -8472-4·154·(-33)
Δ = 737737
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:

$\sqrt{\Delta}=\sqrt{737737}=\sqrt{121*6097}=\sqrt{121}*\sqrt{6097}=11\sqrt{6097}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-847)-11\sqrt{6097}}{2*154}=\frac{847-11\sqrt{6097}}{308}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-847)+11\sqrt{6097}}{2*154}=\frac{847+11\sqrt{6097}}{308}
$