5.3x+2-4/1x=3.6-1.6

Solution for 5.3x+2-4/1x=3.6-1.6 equation:

5.3x+2-4/1x=3.6-1.6

We move all terms to the left:

5.3x+2-4/1x-(3.6-1.6)=0


Domain of the equation: 1x!=0

x∈R


We add all the numbers together, and all the variables

5.3x-4/1x+2-2=0

We add all the numbers together, and all the variables

5.3x-4/1x=0

We multiply all the terms by the denominator


(5.3x)*1x-4=0

We add all the numbers together, and all the variables

(+5.3x)*1x-4=0

We multiply parentheses

5x^2-4=0

a = 5; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·5·(-4)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*5}=\frac{0-4\sqrt{5}}{10}
=-\frac{4\sqrt{5}}{10}
=-\frac{2\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*5}=\frac{0+4\sqrt{5}}{10}
=\frac{4\sqrt{5}}{10}
=\frac{2\sqrt{5}}{5}
$