12x=5/4x+3

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

12x=5/4x+3

We move all terms to the left:

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


Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

12x-5/4x-3=0

We multiply all the terms by the denominator


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

Wy multiply elements

48x^2-12x-5=0

a = 48; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·48·(-5)
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{69}}{2*48}=\frac{12-4\sqrt{69}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{69}}{2*48}=\frac{12+4\sqrt{69}}{96}
$