9y-12=1/4y-4

Solution for 9y-12=1/4y-4 equation:

9y-12=1/4y-4

We move all terms to the left:

9y-12-(1/4y-4)=0


Domain of the equation: 4y-4)!=0

y∈R


We get rid of parentheses

9y-1/4y+4-12=0

We multiply all the terms by the denominator


9y*4y+4*4y-12*4y-1=0

Wy multiply elements

36y^2+16y-48y-1=0

We add all the numbers together, and all the variables

36y^2-32y-1=0

a = 36; b = -32; c = -1;
Δ = b2-4ac
Δ = -322-4·36·(-1)
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{73}}{2*36}=\frac{32-4\sqrt{73}}{72}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{73}}{2*36}=\frac{32+4\sqrt{73}}{72}
$