(1/4)(12x+8)=20

Solution for (1/4)(12x+8)=20 equation:

(1/4)(12x+8)=20

We move all terms to the left:

(1/4)(12x+8)-(20)=0


Domain of the equation: 4)(12x+8)!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)(12x+8)-20=0

We multiply parentheses ..

(+12x^2+1/4*8)-20=0

We multiply all the terms by the denominator


(+12x^2+1-20*4*8)=0

We get rid of parentheses

12x^2+1-20*4*8=0

We add all the numbers together, and all the variables

12x^2-639=0

a = 12; b = 0; c = -639;
Δ = b2-4ac
Δ = 02-4·12·(-639)
Δ = 30672
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:

$\sqrt{\Delta}=\sqrt{30672}=\sqrt{144*213}=\sqrt{144}*\sqrt{213}=12\sqrt{213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{213}}{2*12}=\frac{0-12\sqrt{213}}{24}
=-\frac{12\sqrt{213}}{24}
=-\frac{\sqrt{213}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{213}}{2*12}=\frac{0+12\sqrt{213}}{24}
=\frac{12\sqrt{213}}{24}
=\frac{\sqrt{213}}{2}
$