7+4x=2/3x+5

Solution for 7+4x=2/3x+5 equation:

7+4x=2/3x+5

We move all terms to the left:

7+4x-(2/3x+5)=0


Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

4x-2/3x-5+7=0

We multiply all the terms by the denominator


4x*3x-5*3x+7*3x-2=0

Wy multiply elements

12x^2-15x+21x-2=0

We add all the numbers together, and all the variables

12x^2+6x-2=0

a = 12; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·12·(-2)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{33}}{2*12}=\frac{-6-2\sqrt{33}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{33}}{2*12}=\frac{-6+2\sqrt{33}}{24}
$