10x-27/3=7/3x-5

Solution for 10x-27/3=7/3x-5 equation:

10x-27/3=7/3x-5

We move all terms to the left:

10x-27/3-(7/3x-5)=0


Domain of the equation: 3x-5)!=0

x∈R


We add all the numbers together, and all the variables

10x-(7/3x-5)-9=0

We get rid of parentheses

10x-7/3x+5-9=0

We multiply all the terms by the denominator


10x*3x+5*3x-9*3x-7=0

Wy multiply elements

30x^2+15x-27x-7=0

We add all the numbers together, and all the variables

30x^2-12x-7=0

a = 30; b = -12; c = -7;
Δ = b2-4ac
Δ = -122-4·30·(-7)
Δ = 984
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:

$\sqrt{\Delta}=\sqrt{984}=\sqrt{4*246}=\sqrt{4}*\sqrt{246}=2\sqrt{246}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{246}}{2*30}=\frac{12-2\sqrt{246}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{246}}{2*30}=\frac{12+2\sqrt{246}}{60}
$