12x+3/4x=20

Solution for 12x+3/4x=20 equation:

12x+3/4x=20

We move all terms to the left:

12x+3/4x-(20)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


12x*4x-20*4x+3=0

Wy multiply elements

48x^2-80x+3=0

a = 48; b = -80; c = +3;
Δ = b2-4ac
Δ = -802-4·48·3
Δ = 5824
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:

$\sqrt{\Delta}=\sqrt{5824}=\sqrt{64*91}=\sqrt{64}*\sqrt{91}=8\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{91}}{2*48}=\frac{80-8\sqrt{91}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{91}}{2*48}=\frac{80+8\sqrt{91}}{96}
$