4y=38-(-1/2)(4y+16)

Solution for 4y=38-(-1/2)(4y+16) equation:

4y=38-(-1/2)(4y+16)

We move all terms to the left:

4y-(38-(-1/2)(4y+16))=0


Domain of the equation: 2)(4y+16))!=0

y∈R


We multiply parentheses ..

-(38-(-4y^2-1/2*16))+4y=0

We multiply all the terms by the denominator


-(38-(-4y^2-1+4y*2*16))=0


We calculate terms in parentheses: -(38-(-4y^2-1+4y*2*16)), so:

38-(-4y^2-1+4y*2*16)

determiningTheFunctionDomain
-(-4y^2-1+4y*2*16)+38

We get rid of parentheses

4y^2-4y*2*16+1+38

We add all the numbers together, and all the variables

4y^2-4y*2*16+39

Wy multiply elements

4y^2-128y*1+39

Wy multiply elements

4y^2-128y+39

Back to the equation:

-(4y^2-128y+39)


We get rid of parentheses

-4y^2+128y-39=0

a = -4; b = 128; c = -39;
Δ = b2-4ac
Δ = 1282-4·(-4)·(-39)
Δ = 15760
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:

$\sqrt{\Delta}=\sqrt{15760}=\sqrt{16*985}=\sqrt{16}*\sqrt{985}=4\sqrt{985}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-4\sqrt{985}}{2*-4}=\frac{-128-4\sqrt{985}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+4\sqrt{985}}{2*-4}=\frac{-128+4\sqrt{985}}{-8}
$