9y+8=1/2y-4

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

9y+8=1/2y-4

We move all terms to the left:

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


Domain of the equation: 2y-4)!=0

y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

18y^2+8y+16y-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}
$