3/8y+3/4y+1/2=6

Solution for 3/8y+3/4y+1/2=6 equation:

3/8y+3/4y+1/2=6

We move all terms to the left:

3/8y+3/4y+1/2-(6)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R



Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


determiningTheFunctionDomain
3/8y+3/4y-6+1/2=0

We calculate fractions


128y^2/128y^2+48y/128y^2+96y/128y^2-6=0

Fractions to decimals

48y/128y^2+96y/128y^2-6+1=0

We multiply all the terms by the denominator


48y+96y-6*128y^2+1*128y^2=0

We add all the numbers together, and all the variables

144y-6*128y^2+1*128y^2=0

Wy multiply elements

-768y^2+128y^2+144y=0

We add all the numbers together, and all the variables

-640y^2+144y=0

a = -640; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·(-640)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*-640}=\frac{-288}{-1280}
=9/40
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-640}=\frac{0}{-1280}
=0
$