4x+6=2/3*(9x)

Solution for 4x+6=2/3*(9x) equation:

4x+6=2/3(9x)

We move all terms to the left:

4x+6-(2/3(9x))=0


Domain of the equation: 39x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+2/39x)+6=0

We get rid of parentheses

4x-2/39x+6=0

We multiply all the terms by the denominator


4x*39x+6*39x-2=0

Wy multiply elements

156x^2+234x-2=0

a = 156; b = 234; c = -2;
Δ = b2-4ac
Δ = 2342-4·156·(-2)
Δ = 56004
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:

$\sqrt{\Delta}=\sqrt{56004}=\sqrt{4*14001}=\sqrt{4}*\sqrt{14001}=2\sqrt{14001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(234)-2\sqrt{14001}}{2*156}=\frac{-234-2\sqrt{14001}}{312}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(234)+2\sqrt{14001}}{2*156}=\frac{-234+2\sqrt{14001}}{312}
$