4.6+1.2x=54.6/0.8x

Solution for 4.6+1.2x=54.6/0.8x equation:

4.6+1.2x=54.6/0.8x

We move all terms to the left:

4.6+1.2x-(54.6/0.8x)=0


Domain of the equation: 0.8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1.2x-(+54.6/0.8x)+4.6=0

We get rid of parentheses

1.2x-54.6/0.8x+4.6=0

We multiply all the terms by the denominator


(1.2x)*0.8x+(4.6)*0.8x-54.6=0

We add all the numbers together, and all the variables

(+1.2x)*0.8x+(4.6)*0.8x-54.6=0

We multiply parentheses

0x^2+0x-54.6=0

We add all the numbers together, and all the variables

x^2+x-54.6=0

a = 1; b = 1; c = -54.6;
Δ = b2-4ac
Δ = 12-4·1·(-54.6)
Δ = 219.4
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{-(1)-\sqrt{219.4}}{2*1}=\frac{-1-\sqrt{219.4}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{219.4}}{2*1}=\frac{-1+\sqrt{219.4}}{2}
$