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

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

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

We move all terms to the left:

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


Domain of the equation: 3)(9x+3)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

(+9x^2+1/3*3)-3x-4=0

We multiply all the terms by the denominator


(+9x^2+1-3x*3*3)-4*3*3)=0

We add all the numbers together, and all the variables

(+9x^2+1-3x*3*3)=0

We get rid of parentheses

9x^2-3x*3*3+1=0

Wy multiply elements

9x^2-27x*3+1=0

Wy multiply elements

9x^2-81x+1=0

a = 9; b = -81; c = +1;
Δ = b2-4ac
Δ = -812-4·9·1
Δ = 6525
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:

$\sqrt{\Delta}=\sqrt{6525}=\sqrt{225*29}=\sqrt{225}*\sqrt{29}=15\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-15\sqrt{29}}{2*9}=\frac{81-15\sqrt{29}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+15\sqrt{29}}{2*9}=\frac{81+15\sqrt{29}}{18}
$