12x-3/4x-5=0

Solution for 12x-3/4x-5=0 equation:

12x-3/4x-5=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

48x^2-20x-3=0

a = 48; b = -20; c = -3;
Δ = b2-4ac
Δ = -202-4·48·(-3)
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{61}}{2*48}=\frac{20-4\sqrt{61}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{61}}{2*48}=\frac{20+4\sqrt{61}}{96}
$