2/7a+2a=22

Solution for 2/7a+2a=22 equation:

2/7a+2a=22

We move all terms to the left:

2/7a+2a-(22)=0


Domain of the equation: 7a!=0

a!=0/7

a!=0

a∈R


We add all the numbers together, and all the variables

2a+2/7a-22=0

We multiply all the terms by the denominator


2a*7a-22*7a+2=0

Wy multiply elements

14a^2-154a+2=0

a = 14; b = -154; c = +2;
Δ = b2-4ac
Δ = -1542-4·14·2
Δ = 23604
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:

$\sqrt{\Delta}=\sqrt{23604}=\sqrt{4*5901}=\sqrt{4}*\sqrt{5901}=2\sqrt{5901}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-154)-2\sqrt{5901}}{2*14}=\frac{154-2\sqrt{5901}}{28}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-154)+2\sqrt{5901}}{2*14}=\frac{154+2\sqrt{5901}}{28}
$