(1/4)(2x+1)=26

Solution for (1/4)(2x+1)=26 equation:

(1/4)(2x+1)=26

We move all terms to the left:

(1/4)(2x+1)-(26)=0


Domain of the equation: 4)(2x+1)!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)(2x+1)-26=0

We multiply parentheses ..

(+2x^2+1/4*1)-26=0

We multiply all the terms by the denominator


(+2x^2+1-26*4*1)=0

We get rid of parentheses

2x^2+1-26*4*1=0

We add all the numbers together, and all the variables

2x^2-103=0

a = 2; b = 0; c = -103;
Δ = b2-4ac
Δ = 02-4·2·(-103)
Δ = 824
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:

$\sqrt{\Delta}=\sqrt{824}=\sqrt{4*206}=\sqrt{4}*\sqrt{206}=2\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{206}}{2*2}=\frac{0-2\sqrt{206}}{4}
=-\frac{2\sqrt{206}}{4}
=-\frac{\sqrt{206}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{206}}{2*2}=\frac{0+2\sqrt{206}}{4}
=\frac{2\sqrt{206}}{4}
=\frac{\sqrt{206}}{2}
$