-2/3y-1/8y=456

Solution for -2/3y-1/8y=456 equation:

-2/3y-1/8y=456

We move all terms to the left:

-2/3y-1/8y-(456)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We calculate fractions


(-16y)/24y^2+(-3y)/24y^2-456=0

We multiply all the terms by the denominator


(-16y)+(-3y)-456*24y^2=0

Wy multiply elements

-10944y^2+(-16y)+(-3y)=0

We get rid of parentheses

-10944y^2-16y-3y=0

We add all the numbers together, and all the variables

-10944y^2-19y=0

a = -10944; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-10944)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-10944}=\frac{0}{-21888}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-10944}=\frac{38}{-21888}
=-1/576
$