7/3x-6=x+10

Solution for 7/3x-6=x+10 equation:

7/3x-6=x+10

We move all terms to the left:

7/3x-6-(x+10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

7/3x-x-10-6=0

We multiply all the terms by the denominator


-x*3x-10*3x-6*3x+7=0

Wy multiply elements

-3x^2-30x-18x+7=0

We add all the numbers together, and all the variables

-3x^2-48x+7=0

a = -3; b = -48; c = +7;
Δ = b2-4ac
Δ = -482-4·(-3)·7
Δ = 2388
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:

$\sqrt{\Delta}=\sqrt{2388}=\sqrt{4*597}=\sqrt{4}*\sqrt{597}=2\sqrt{597}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{597}}{2*-3}=\frac{48-2\sqrt{597}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{597}}{2*-3}=\frac{48+2\sqrt{597}}{-6}
$