4x+5=2/3(9x)

Solution for 4x+5=2/3(9x) equation:

4x+5=2/3(9x)

We move all terms to the left:

4x+5-(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)+5=0

We get rid of parentheses

4x-2/39x+5=0

We multiply all the terms by the denominator


4x*39x+5*39x-2=0

Wy multiply elements

156x^2+195x-2=0

a = 156; b = 195; c = -2;
Δ = b2-4ac
Δ = 1952-4·156·(-2)
Δ = 39273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(195)-\sqrt{39273}}{2*156}=\frac{-195-\sqrt{39273}}{312}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(195)+\sqrt{39273}}{2*156}=\frac{-195+\sqrt{39273}}{312}
$