5x=4/55x-2

Solution for 5x=4/55x-2 equation:

5x=4/55x-2

We move all terms to the left:

5x-(4/55x-2)=0


Domain of the equation: 55x-2)!=0

x∈R


We get rid of parentheses

5x-4/55x+2=0

We multiply all the terms by the denominator


5x*55x+2*55x-4=0

Wy multiply elements

275x^2+110x-4=0

a = 275; b = 110; c = -4;
Δ = b2-4ac
Δ = 1102-4·275·(-4)
Δ = 16500
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:

$\sqrt{\Delta}=\sqrt{16500}=\sqrt{100*165}=\sqrt{100}*\sqrt{165}=10\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-10\sqrt{165}}{2*275}=\frac{-110-10\sqrt{165}}{550}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+10\sqrt{165}}{2*275}=\frac{-110+10\sqrt{165}}{550}
$