4+2/3x-4=7x+124

Solution for 4+2/3x-4=7x+124 equation:

4+2/3x-4=7x+124

We move all terms to the left:

4+2/3x-4-(7x+124)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(7x+124)=0

We get rid of parentheses

2/3x-7x-124=0

We multiply all the terms by the denominator


-7x*3x-124*3x+2=0

Wy multiply elements

-21x^2-372x+2=0

a = -21; b = -372; c = +2;
Δ = b2-4ac
Δ = -3722-4·(-21)·2
Δ = 138552
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:

$\sqrt{\Delta}=\sqrt{138552}=\sqrt{4*34638}=\sqrt{4}*\sqrt{34638}=2\sqrt{34638}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-372)-2\sqrt{34638}}{2*-21}=\frac{372-2\sqrt{34638}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-372)+2\sqrt{34638}}{2*-21}=\frac{372+2\sqrt{34638}}{-42}
$