2/3x-7=35-4x

Solution for 2/3x-7=35-4x equation:

2/3x-7=35-4x

We move all terms to the left:

2/3x-7-(35-4x)=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-(-4x+35)-7=0

We get rid of parentheses

2/3x+4x-35-7=0

We multiply all the terms by the denominator


4x*3x-35*3x-7*3x+2=0

Wy multiply elements

12x^2-105x-21x+2=0

We add all the numbers together, and all the variables

12x^2-126x+2=0

a = 12; b = -126; c = +2;
Δ = b2-4ac
Δ = -1262-4·12·2
Δ = 15780
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:

$\sqrt{\Delta}=\sqrt{15780}=\sqrt{4*3945}=\sqrt{4}*\sqrt{3945}=2\sqrt{3945}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{3945}}{2*12}=\frac{126-2\sqrt{3945}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{3945}}{2*12}=\frac{126+2\sqrt{3945}}{24}
$