12x+5=3/4x+1

Solution for 12x+5=3/4x+1 equation:

12x+5=3/4x+1

We move all terms to the left:

12x+5-(3/4x+1)=0


Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

12x-3/4x-1+5=0

We multiply all the terms by the denominator


12x*4x-1*4x+5*4x-3=0

Wy multiply elements

48x^2-4x+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}
$