10x-27/3=7/3x-55

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Solution for 10x-27/3=7/3x-55 equation: 



10x-27/3=7/3x-55

We move all terms to the left:

10x-27/3-(7/3x-55)=0



Domain of the equation: 3x-55)!=0

x∈R



We add all the numbers together, and all the variables

10x-(7/3x-55)-9=0

We get rid of parentheses

10x-7/3x+55-9=0

We multiply all the terms by the denominator


10x*3x+55*3x-9*3x-7=0

Wy multiply elements

30x^2+165x-27x-7=0

We add all the numbers together, and all the variables

30x^2+138x-7=0

a = 30; b = 138; c = -7;
Δ = b2-4ac
Δ = 1382-4·30·(-7)
Δ = 19884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:


$\sqrt{\Delta}=\sqrt{19884}=\sqrt{4*4971}=\sqrt{4}*\sqrt{4971}=2\sqrt{4971}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(138)-2\sqrt{4971}}{2*30}=\frac{-138-2\sqrt{4971}}{60}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(138)+2\sqrt{4971}}{2*30}=\frac{-138+2\sqrt{4971}}{60}
$

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