(1/4)(y+9)-5=12

Solution for (1/4)(y+9)-5=12 equation:

(1/4)(y+9)-5=12

We move all terms to the left:

(1/4)(y+9)-5-(12)=0


Domain of the equation: 4)(y+9)!=0

y∈R


We add all the numbers together, and all the variables

(+1/4)(y+9)-5-12=0

We add all the numbers together, and all the variables

(+1/4)(y+9)-17=0

We multiply parentheses ..

(+y^2+1/4*9)-17=0

We multiply all the terms by the denominator


(+y^2+1-17*4*9)=0

We get rid of parentheses

y^2+1-17*4*9=0

We add all the numbers together, and all the variables

y^2-611=0

a = 1; b = 0; c = -611;
Δ = b2-4ac
Δ = 02-4·1·(-611)
Δ = 2444
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:

$\sqrt{\Delta}=\sqrt{2444}=\sqrt{4*611}=\sqrt{4}*\sqrt{611}=2\sqrt{611}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{611}}{2*1}=\frac{0-2\sqrt{611}}{2}
=-\frac{2\sqrt{611}}{2}
=-\sqrt{611}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{611}}{2*1}=\frac{0+2\sqrt{611}}{2}
=\frac{2\sqrt{611}}{2}
=\sqrt{611}
$