182=3x+11/5x

Solution for 182=3x+11/5x equation:

182=3x+11/5x

We move all terms to the left:

182-(3x+11/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+3x+11/5x)+182=0

We get rid of parentheses

-3x-11/5x+182=0

We multiply all the terms by the denominator


-3x*5x+182*5x-11=0

Wy multiply elements

-15x^2+910x-11=0

a = -15; b = 910; c = -11;
Δ = b2-4ac
Δ = 9102-4·(-15)·(-11)
Δ = 827440
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:

$\sqrt{\Delta}=\sqrt{827440}=\sqrt{16*51715}=\sqrt{16}*\sqrt{51715}=4\sqrt{51715}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(910)-4\sqrt{51715}}{2*-15}=\frac{-910-4\sqrt{51715}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(910)+4\sqrt{51715}}{2*-15}=\frac{-910+4\sqrt{51715}}{-30}
$