3(2x+1)+1/4(3x)=9

Solution for 3(2x+1)+1/4(3x)=9 equation:

3(2x+1)+1/4(3x)=9

We move all terms to the left:

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


Domain of the equation: 43x!=0

x!=0/43

x!=0

x∈R


We multiply parentheses

6x+1/43x+3-9=0

We multiply all the terms by the denominator


6x*43x+3*43x-9*43x+1=0

Wy multiply elements

258x^2+129x-387x+1=0

We add all the numbers together, and all the variables

258x^2-258x+1=0

a = 258; b = -258; c = +1;
Δ = b2-4ac
Δ = -2582-4·258·1
Δ = 65532
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:

$\sqrt{\Delta}=\sqrt{65532}=\sqrt{4*16383}=\sqrt{4}*\sqrt{16383}=2\sqrt{16383}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-258)-2\sqrt{16383}}{2*258}=\frac{258-2\sqrt{16383}}{516}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-258)+2\sqrt{16383}}{2*258}=\frac{258+2\sqrt{16383}}{516}
$