1/4y-9y=14

Solution for 1/4y-9y=14 equation:

1/4y-9y=14

We move all terms to the left:

1/4y-9y-(14)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

-9y+1/4y-14=0

We multiply all the terms by the denominator


-9y*4y-14*4y+1=0

Wy multiply elements

-36y^2-56y+1=0

a = -36; b = -56; c = +1;
Δ = b2-4ac
Δ = -562-4·(-36)·1
Δ = 3280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{205}}{2*-36}=\frac{56-4\sqrt{205}}{-72}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{205}}{2*-36}=\frac{56+4\sqrt{205}}{-72}
$