1/3(9x)=4x+5

Solution for 1/3(9x)=4x+5 equation:

1/3(9x)=4x+5

We move all terms to the left:

1/3(9x)-(4x+5)=0


Domain of the equation: 39x!=0

x!=0/39

x!=0

x∈R


We get rid of parentheses

1/39x-4x-5=0

We multiply all the terms by the denominator


-4x*39x-5*39x+1=0

Wy multiply elements

-156x^2-195x+1=0

a = -156; b = -195; c = +1;
Δ = b2-4ac
Δ = -1952-4·(-156)·1
Δ = 38649
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{38649}}{2*-156}=\frac{195-\sqrt{38649}}{-312}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-195)+\sqrt{38649}}{2*-156}=\frac{195+\sqrt{38649}}{-312}
$