1/5x+3+4x=12

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

1/5x+3+4x=12

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/5x-9=0

We multiply all the terms by the denominator


4x*5x-9*5x+1=0

Wy multiply elements

20x^2-45x+1=0

a = 20; b = -45; c = +1;
Δ = b2-4ac
Δ = -452-4·20·1
Δ = 1945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{1945}}{2*20}=\frac{45-\sqrt{1945}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1945}}{2*20}=\frac{45+\sqrt{1945}}{40}
$