3/4x+5=12x+9

Solution for 3/4x+5=12x+9 equation:

3/4x+5=12x+9

We move all terms to the left:

3/4x+5-(12x+9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-12x-9+5=0

We multiply all the terms by the denominator


-12x*4x-9*4x+5*4x+3=0

Wy multiply elements

-48x^2-36x+20x+3=0

We add all the numbers together, and all the variables

-48x^2-16x+3=0

a = -48; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·(-48)·3
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{13}}{2*-48}=\frac{16-8\sqrt{13}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{13}}{2*-48}=\frac{16+8\sqrt{13}}{-96}
$