(13/4y)-(4y)=18

Solution for (13/4y)-(4y)=18 equation:

(13/4y)-(4y)=18

We move all terms to the left:

(13/4y)-(4y)-(18)=0


Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+13/4y)-4y-18=0

We add all the numbers together, and all the variables

-4y+(+13/4y)-18=0

We get rid of parentheses

-4y+13/4y-18=0

We multiply all the terms by the denominator


-4y*4y-18*4y+13=0

Wy multiply elements

-16y^2-72y+13=0

a = -16; b = -72; c = +13;
Δ = b2-4ac
Δ = -722-4·(-16)·13
Δ = 6016
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:

$\sqrt{\Delta}=\sqrt{6016}=\sqrt{64*94}=\sqrt{64}*\sqrt{94}=8\sqrt{94}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{94}}{2*-16}=\frac{72-8\sqrt{94}}{-32}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{94}}{2*-16}=\frac{72+8\sqrt{94}}{-32}
$