-9/4y-9=-4y+8

Solution for -9/4y-9=-4y+8 equation:

-9/4y-9=-4y+8

We move all terms to the left:

-9/4y-9-(-4y+8)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We get rid of parentheses

-9/4y+4y-8-9=0

We multiply all the terms by the denominator


4y*4y-8*4y-9*4y-9=0

Wy multiply elements

16y^2-32y-36y-9=0

We add all the numbers together, and all the variables

16y^2-68y-9=0

a = 16; b = -68; c = -9;
Δ = b2-4ac
Δ = -682-4·16·(-9)
Δ = 5200
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:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-20\sqrt{13}}{2*16}=\frac{68-20\sqrt{13}}{32}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+20\sqrt{13}}{2*16}=\frac{68+20\sqrt{13}}{32}
$