(1/4)(8y+36)=44

Solution for (1/4)(8y+36)=44 equation:

(1/4)(8y+36)=44

We move all terms to the left:

(1/4)(8y+36)-(44)=0


Domain of the equation: 4)(8y+36)!=0

y∈R


We add all the numbers together, and all the variables

(+1/4)(8y+36)-44=0

We multiply parentheses ..

(+8y^2+1/4*36)-44=0

We multiply all the terms by the denominator


(+8y^2+1-44*4*36)=0

We get rid of parentheses

8y^2+1-44*4*36=0

We add all the numbers together, and all the variables

8y^2-6335=0

a = 8; b = 0; c = -6335;
Δ = b2-4ac
Δ = 02-4·8·(-6335)
Δ = 202720
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:

$\sqrt{\Delta}=\sqrt{202720}=\sqrt{16*12670}=\sqrt{16}*\sqrt{12670}=4\sqrt{12670}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{12670}}{2*8}=\frac{0-4\sqrt{12670}}{16}
=-\frac{4\sqrt{12670}}{16}
=-\frac{\sqrt{12670}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{12670}}{2*8}=\frac{0+4\sqrt{12670}}{16}
=\frac{4\sqrt{12670}}{16}
=\frac{\sqrt{12670}}{4}
$