-3/8(-6-2y)=1/2(2y-10)

Solution for -3/8(-6-2y)=1/2(2y-10) equation:

-3/8(-6-2y)=1/2(2y-10)

We move all terms to the left:

-3/8(-6-2y)-(1/2(2y-10))=0


Domain of the equation: 8(-6-2y)!=0

y∈R



Domain of the equation: 2(2y-10))!=0

y∈R


We add all the numbers together, and all the variables

-3/8(-2y-6)-(1/2(2y-10))=0

We calculate fractions


(-6y2/(8(-2y-6)*2(2y-10)))+(-8y0/(8(-2y-6)*2(2y-10)))=0


We calculate terms in parentheses: +(-6y2/(8(-2y-6)*2(2y-10))), so:

-6y2/(8(-2y-6)*2(2y-10))

We multiply all the terms by the denominator


-6y2

We add all the numbers together, and all the variables

-6y^2

Back to the equation:

+(-6y^2)



We calculate terms in parentheses: +(-8y0/(8(-2y-6)*2(2y-10))), so:

-8y0/(8(-2y-6)*2(2y-10))

We multiply all the terms by the denominator


-8y0

We add all the numbers together, and all the variables

-8y

Back to the equation:

+(-8y)


We get rid of parentheses

-6y^2-8y=0

a = -6; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-6)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-6}=\frac{0}{-12}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-6}=\frac{16}{-12}
=-1+1/3
$