1/5x+5.34=2.2x+1.54

Solution for 1/5x+5.34=2.2x+1.54 equation:

1/5x+5.34=2.2x+1.54

We move all terms to the left:

1/5x+5.34-(2.2x+1.54)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-2.2x-1.54+5.34=0

We multiply all the terms by the denominator


-(2.2x)*5x-(1.54)*5x+(5.34)*5x+1=0

We add all the numbers together, and all the variables

-(+2.2x)*5x-(1.54)*5x+(5.34)*5x+1=0

We multiply parentheses

-10x^2-7.7x+26.7x+1=0

We add all the numbers together, and all the variables

-10x^2+19x+1=0

a = -10; b = 19; c = +1;
Δ = b2-4ac
Δ = 192-4·(-10)·1
Δ = 401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{401}}{2*-10}=\frac{-19-\sqrt{401}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{401}}{2*-10}=\frac{-19+\sqrt{401}}{-20}
$