(1/4)(4x+8)=5

Solution for (1/4)(4x+8)=5 equation:

(1/4)(4x+8)=5

We move all terms to the left:

(1/4)(4x+8)-(5)=0


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

x∈R


We add all the numbers together, and all the variables

(+1/4)(4x+8)-5=0

We multiply parentheses ..

(+4x^2+1/4*8)-5=0

We multiply all the terms by the denominator


(+4x^2+1-5*4*8)=0

We get rid of parentheses

4x^2+1-5*4*8=0

We add all the numbers together, and all the variables

4x^2-159=0

a = 4; b = 0; c = -159;
Δ = b2-4ac
Δ = 02-4·4·(-159)
Δ = 2544
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:

$\sqrt{\Delta}=\sqrt{2544}=\sqrt{16*159}=\sqrt{16}*\sqrt{159}=4\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{159}}{2*4}=\frac{0-4\sqrt{159}}{8}
=-\frac{4\sqrt{159}}{8}
=-\frac{\sqrt{159}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{159}}{2*4}=\frac{0+4\sqrt{159}}{8}
=\frac{4\sqrt{159}}{8}
=\frac{\sqrt{159}}{2}
$