1/2y-4=9y+8

Solution for 1/2y-4=9y+8 equation:

1/2y-4=9y+8

We move all terms to the left:

1/2y-4-(9y+8)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

1/2y-9y-8-4=0

We multiply all the terms by the denominator


-9y*2y-8*2y-4*2y+1=0

Wy multiply elements

-18y^2-16y-8y+1=0

We add all the numbers together, and all the variables

-18y^2-24y+1=0

a = -18; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·(-18)·1
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-18\sqrt{2}}{2*-18}=\frac{24-18\sqrt{2}}{-36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+18\sqrt{2}}{2*-18}=\frac{24+18\sqrt{2}}{-36}
$