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

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+192x-7=0

a = 30; b = 192; c = -7;
Δ = b2-4ac
Δ = 1922-4·30·(-7)
Δ = 37704
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:

$\sqrt{\Delta}=\sqrt{37704}=\sqrt{4*9426}=\sqrt{4}*\sqrt{9426}=2\sqrt{9426}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-2\sqrt{9426}}{2*30}=\frac{-192-2\sqrt{9426}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+2\sqrt{9426}}{2*30}=\frac{-192+2\sqrt{9426}}{60}
$