y/4=18+y/8y+4

Solution for y/4=18+y/8y+4 equation:

y/4=18+y/8y+4

We move all terms to the left:

y/4-(18+y/8y+4)=0


Domain of the equation: 8y+4)!=0

y∈R


We add all the numbers together, and all the variables

y/4-(y/8y+22)=0

We get rid of parentheses

y/4-y/8y-22=0

We calculate fractions


8y^2/32y+(-4y)/32y-22=0

We multiply all the terms by the denominator


8y^2+(-4y)-22*32y=0

Wy multiply elements

8y^2+(-4y)-704y=0

We get rid of parentheses

8y^2-4y-704y=0

We add all the numbers together, and all the variables

8y^2-708y=0

a = 8; b = -708; c = 0;
Δ = b2-4ac
Δ = -7082-4·8·0
Δ = 501264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{501264}=708$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-708)-708}{2*8}=\frac{0}{16}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-708)+708}{2*8}=\frac{1416}{16}
=88+1/2
$