5.5x-3.3=1/5x-12

Solution for 5.5x-3.3=1/5x-12 equation:

5.5x-3.3=1/5x-12

We move all terms to the left:

5.5x-3.3-(1/5x-12)=0


Domain of the equation: 5x-12)!=0

x∈R


We get rid of parentheses

5.5x-1/5x+12-3.3=0

We multiply all the terms by the denominator


(5.5x)*5x+12*5x-(3.3)*5x-1=0

We add all the numbers together, and all the variables

(+5.5x)*5x+12*5x-(3.3)*5x-1=0

We multiply parentheses

25x^2+12*5x-16.5x-1=0

Wy multiply elements

25x^2+60x-16.5x-1=0

We add all the numbers together, and all the variables

25x^2+43.5x-1=0

a = 25; b = 43.5; c = -1;
Δ = b2-4ac
Δ = 43.52-4·25·(-1)
Δ = 1992.25
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{-(43.5)-\sqrt{1992.25}}{2*25}=\frac{-43.5-\sqrt{1992.25}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43.5)+\sqrt{1992.25}}{2*25}=\frac{-43.5+\sqrt{1992.25}}{50}
$