(1/4)(8x+20)=27

Solution for (1/4)(8x+20)=27 equation:

(1/4)(8x+20)=27

We move all terms to the left:

(1/4)(8x+20)-(27)=0


Domain of the equation: 4)(8x+20)!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)(8x+20)-27=0

We multiply parentheses ..

(+8x^2+1/4*20)-27=0

We multiply all the terms by the denominator


(+8x^2+1-27*4*20)=0

We get rid of parentheses

8x^2+1-27*4*20=0

We add all the numbers together, and all the variables

8x^2-2159=0

a = 8; b = 0; c = -2159;
Δ = b2-4ac
Δ = 02-4·8·(-2159)
Δ = 69088
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{69088}=\sqrt{16*4318}=\sqrt{16}*\sqrt{4318}=4\sqrt{4318}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{4318}}{2*8}=\frac{0-4\sqrt{4318}}{16}
=-\frac{4\sqrt{4318}}{16}
=-\frac{\sqrt{4318}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{4318}}{2*8}=\frac{0+4\sqrt{4318}}{16}
=\frac{4\sqrt{4318}}{16}
=\frac{\sqrt{4318}}{4}
$