y-3/4y=18

Solution for y-3/4y=18 equation:

y-3/4y=18

We move all terms to the left:

y-3/4y-(18)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We multiply all the terms by the denominator


y*4y-18*4y-3=0

Wy multiply elements

4y^2-72y-3=0

a = 4; b = -72; c = -3;
Δ = b2-4ac
Δ = -722-4·4·(-3)
Δ = 5232
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:

$\sqrt{\Delta}=\sqrt{5232}=\sqrt{16*327}=\sqrt{16}*\sqrt{327}=4\sqrt{327}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{327}}{2*4}=\frac{72-4\sqrt{327}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{327}}{2*4}=\frac{72+4\sqrt{327}}{8}
$