4/9y-8=-4y=

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

4/9y-8=-4y=

We move all terms to the left:

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


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R


We get rid of parentheses

4/9y+4y-8=0

We multiply all the terms by the denominator


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

Wy multiply elements

36y^2-72y+4=0

a = 36; b = -72; c = +4;
Δ = b2-4ac
Δ = -722-4·36·4
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-48\sqrt{2}}{2*36}=\frac{72-48\sqrt{2}}{72}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+48\sqrt{2}}{2*36}=\frac{72+48\sqrt{2}}{72}
$