(1/2)(y+1)=9

Solution for (1/2)(y+1)=9 equation:

(1/2)(y+1)=9

We move all terms to the left:

(1/2)(y+1)-(9)=0


Domain of the equation: 2)(y+1)!=0

y∈R


We add all the numbers together, and all the variables

(+1/2)(y+1)-9=0

We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We get rid of parentheses

y^2+1-9*2*1=0

We add all the numbers together, and all the variables

y^2-17=0

a = 1; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·1·(-17)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{17}}{2*1}=\frac{0-2\sqrt{17}}{2}
=-\frac{2\sqrt{17}}{2}
=-\sqrt{17}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{17}}{2*1}=\frac{0+2\sqrt{17}}{2}
=\frac{2\sqrt{17}}{2}
=\sqrt{17}
$