2.66666666666+3x=4/5x+18

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Solution for 2.66666666666+3x=4/5x+18 equation: 



2.66666666666+3x=4/5x+18

We move all terms to the left:

2.66666666666+3x-(4/5x+18)=0



Domain of the equation: 5x+18)!=0

x∈R



We get rid of parentheses

3x-4/5x-18+2.66666666666=0

We multiply all the terms by the denominator


3x*5x-18*5x+(2.66666666666)*5x-4=0

We multiply parentheses

3x*5x-18*5x+13.3333333333x-4=0

Wy multiply elements

15x^2-90x+13.3333333333x-4=0

We add all the numbers together, and all the variables

15x^2-76.6666666667x-4=0

a = 15; b = -76.6666666667; c = -4;
Δ = b2-4ac
Δ = -76.66666666672-4·15·(-4)
Δ = 6117.77777778
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{-(-76.6666666667)-\sqrt{6117.77777778}}{2*15}=\frac{76.6666666667-\sqrt{6117.77777778}}{30}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76.6666666667)+\sqrt{6117.77777778}}{2*15}=\frac{76.6666666667+\sqrt{6117.77777778}}{30}
$

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