-(1/2)(12y+16)=5y-9

Solution for -(1/2)(12y+16)=5y-9 equation:

-(1/2)(12y+16)=5y-9

We move all terms to the left:

-(1/2)(12y+16)-(5y-9)=0


Domain of the equation: 2)(12y+16)!=0

y∈R


We add all the numbers together, and all the variables

-(+1/2)(12y+16)-(5y-9)=0

We get rid of parentheses

-(+1/2)(12y+16)-5y+9=0

We multiply parentheses ..

-(+12y^2+1/2*16)-5y+9=0

We multiply all the terms by the denominator


-(+12y^2+1-5y*2*16)+9*2*16)=0

We add all the numbers together, and all the variables

-(+12y^2+1-5y*2*16)=0

We get rid of parentheses

-12y^2+5y*2*16-1=0

Wy multiply elements

-12y^2+160y*1-1=0

Wy multiply elements

-12y^2+160y-1=0

a = -12; b = 160; c = -1;
Δ = b2-4ac
Δ = 1602-4·(-12)·(-1)
Δ = 25552
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:

$\sqrt{\Delta}=\sqrt{25552}=\sqrt{16*1597}=\sqrt{16}*\sqrt{1597}=4\sqrt{1597}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-4\sqrt{1597}}{2*-12}=\frac{-160-4\sqrt{1597}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+4\sqrt{1597}}{2*-12}=\frac{-160+4\sqrt{1597}}{-24}
$