(1/4)(7x+1)=4

Solution for (1/4)(7x+1)=4 equation:

(1/4)(7x+1)=4

We move all terms to the left:

(1/4)(7x+1)-(4)=0


Domain of the equation: 4)(7x+1)!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)(7x+1)-4=0

We multiply parentheses ..

(+7x^2+1/4*1)-4=0

We multiply all the terms by the denominator


(+7x^2+1-4*4*1)=0

We get rid of parentheses

7x^2+1-4*4*1=0

We add all the numbers together, and all the variables

7x^2-15=0

a = 7; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·7·(-15)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{105}}{2*7}=\frac{0-2\sqrt{105}}{14}
=-\frac{2\sqrt{105}}{14}
=-\frac{\sqrt{105}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{105}}{2*7}=\frac{0+2\sqrt{105}}{14}
=\frac{2\sqrt{105}}{14}
=\frac{\sqrt{105}}{7}
$