(1/4)(x+8)=12

Solution for (1/4)(x+8)=12 equation:

(1/4)(x+8)=12

We move all terms to the left:

(1/4)(x+8)-(12)=0


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

x∈R


We add all the numbers together, and all the variables

(+1/4)(x+8)-12=0

We multiply parentheses ..

(+x^2+1/4*8)-12=0

We multiply all the terms by the denominator


(+x^2+1-12*4*8)=0

We get rid of parentheses

x^2+1-12*4*8=0

We add all the numbers together, and all the variables

x^2-383=0

a = 1; b = 0; c = -383;
Δ = b2-4ac
Δ = 02-4·1·(-383)
Δ = 1532
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:

$\sqrt{\Delta}=\sqrt{1532}=\sqrt{4*383}=\sqrt{4}*\sqrt{383}=2\sqrt{383}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{383}}{2*1}=\frac{0-2\sqrt{383}}{2}
=-\frac{2\sqrt{383}}{2}
=-\sqrt{383}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{383}}{2*1}=\frac{0+2\sqrt{383}}{2}
=\frac{2\sqrt{383}}{2}
=\sqrt{383}
$