1/8(24y+24)-7=-1/2(2y-8)

Solution for 1/8(24y+24)-7=-1/2(2y-8) equation:

1/8(24y+24)-7=-1/2(2y-8)

We move all terms to the left:

1/8(24y+24)-7-(-1/2(2y-8))=0


Domain of the equation: 8(24y+24)!=0

y∈R



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

y∈R


We calculate fractions


(2y2/(8(24y+24)*2(2y-8)))+(-(-8y2)/(8(24y+24)*2(2y-8)))-7=0


We calculate terms in parentheses: +(2y2/(8(24y+24)*2(2y-8))), so:

2y2/(8(24y+24)*2(2y-8))

We multiply all the terms by the denominator


2y2

We add all the numbers together, and all the variables

2y^2

Back to the equation:

+(2y^2)



We calculate terms in parentheses: +(-(-8y2)/(8(24y+24)*2(2y-8))), so:

-(-8y2)/(8(24y+24)*2(2y-8))

We add all the numbers together, and all the variables

-(-8y^2)/(8(24y+24)*2(2y-8))

We multiply all the terms by the denominator


-(-8y^2)

We get rid of parentheses

8y^2

Back to the equation:

+(8y^2)


We add all the numbers together, and all the variables

10y^2-7=0

a = 10; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·10·(-7)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{70}}{2*10}=\frac{0-2\sqrt{70}}{20}
=-\frac{2\sqrt{70}}{20}
=-\frac{\sqrt{70}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{70}}{2*10}=\frac{0+2\sqrt{70}}{20}
=\frac{2\sqrt{70}}{20}
=\frac{\sqrt{70}}{10}
$