1a+3/4a=14

Solution for 1a+3/4a=14 equation:

1a+3/4a=14

We move all terms to the left:

1a+3/4a-(14)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We add all the numbers together, and all the variables

a+3/4a-14=0

We multiply all the terms by the denominator


a*4a-14*4a+3=0

Wy multiply elements

4a^2-56a+3=0

a = 4; b = -56; c = +3;
Δ = b2-4ac
Δ = -562-4·4·3
Δ = 3088
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3088}=\sqrt{16*193}=\sqrt{16}*\sqrt{193}=4\sqrt{193}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{193}}{2*4}=\frac{56-4\sqrt{193}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{193}}{2*4}=\frac{56+4\sqrt{193}}{8}
$