y-9=24-3/8y

Solution for y-9=24-3/8y equation:

y-9=24-3/8y

We move all terms to the left:

y-9-(24-3/8y)=0


Domain of the equation: 8y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y-(-3/8y+24)-9=0

We get rid of parentheses

y+3/8y-24-9=0

We multiply all the terms by the denominator


y*8y-24*8y-9*8y+3=0

Wy multiply elements

8y^2-192y-72y+3=0

We add all the numbers together, and all the variables

8y^2-264y+3=0

a = 8; b = -264; c = +3;
Δ = b2-4ac
Δ = -2642-4·8·3
Δ = 69600
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:

$\sqrt{\Delta}=\sqrt{69600}=\sqrt{400*174}=\sqrt{400}*\sqrt{174}=20\sqrt{174}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-20\sqrt{174}}{2*8}=\frac{264-20\sqrt{174}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+20\sqrt{174}}{2*8}=\frac{264+20\sqrt{174}}{16}
$