4/3x-3=x+7

Solution for 4/3x-3=x+7 equation:

4/3x-3=x+7

We move all terms to the left:

4/3x-3-(x+7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-x-7-3=0

We multiply all the terms by the denominator


-x*3x-7*3x-3*3x+4=0

Wy multiply elements

-3x^2-21x-9x+4=0

We add all the numbers together, and all the variables

-3x^2-30x+4=0

a = -3; b = -30; c = +4;
Δ = b2-4ac
Δ = -302-4·(-3)·4
Δ = 948
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:

$\sqrt{\Delta}=\sqrt{948}=\sqrt{4*237}=\sqrt{4}*\sqrt{237}=2\sqrt{237}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{237}}{2*-3}=\frac{30-2\sqrt{237}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{237}}{2*-3}=\frac{30+2\sqrt{237}}{-6}
$