3x+3.25=5/6x

Solution for 3x+3.25=5/6x equation:

3x+3.25=5/6x

We move all terms to the left:

3x+3.25-(5/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+5/6x)+3.25=0

We get rid of parentheses

3x-5/6x+3.25=0

We multiply all the terms by the denominator


3x*6x+(3.25)*6x-5=0

We multiply parentheses

3x*6x+19.5x-5=0

Wy multiply elements

18x^2+19.5x-5=0

a = 18; b = 19.5; c = -5;
Δ = b2-4ac
Δ = 19.52-4·18·(-5)
Δ = 740.25
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{-(19.5)-\sqrt{740.25}}{2*18}=\frac{-19.5-\sqrt{740.25}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19.5)+\sqrt{740.25}}{2*18}=\frac{-19.5+\sqrt{740.25}}{36}
$