(1/2)(7a+1)=18

Solution for (1/2)(7a+1)=18 equation:

(1/2)(7a+1)=18

We move all terms to the left:

(1/2)(7a+1)-(18)=0


Domain of the equation: 2)(7a+1)!=0

a∈R


We add all the numbers together, and all the variables

(+1/2)(7a+1)-18=0

We multiply parentheses ..

(+7a^2+1/2*1)-18=0

We multiply all the terms by the denominator


(+7a^2+1-18*2*1)=0

We get rid of parentheses

7a^2+1-18*2*1=0

We add all the numbers together, and all the variables

7a^2-35=0

a = 7; b = 0; c = -35;
Δ = b2-4ac
Δ = 02-4·7·(-35)
Δ = 980
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{980}=\sqrt{196*5}=\sqrt{196}*\sqrt{5}=14\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{5}}{2*7}=\frac{0-14\sqrt{5}}{14}
=-\frac{14\sqrt{5}}{14}
=-\sqrt{5}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{5}}{2*7}=\frac{0+14\sqrt{5}}{14}
=\frac{14\sqrt{5}}{14}
=\sqrt{5}
$