3x-2/3x+10=7

Solution for 3x-2/3x+10=7 equation:

3x-2/3x+10=7

We move all terms to the left:

3x-2/3x+10-(7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x-2/3x+3=0

We multiply all the terms by the denominator


3x*3x+3*3x-2=0

Wy multiply elements

9x^2+9x-2=0

a = 9; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·9·(-2)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{17}}{2*9}=\frac{-9-3\sqrt{17}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{17}}{2*9}=\frac{-9+3\sqrt{17}}{18}
$