5a-2a+4=22/3a

Solution for 5a-2a+4=22/3a equation:

5a-2a+4=22/3a

We move all terms to the left:

5a-2a+4-(22/3a)=0


Domain of the equation: 3a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

5a-2a-(+22/3a)+4=0

We add all the numbers together, and all the variables

3a-(+22/3a)+4=0

We get rid of parentheses

3a-22/3a+4=0

We multiply all the terms by the denominator


3a*3a+4*3a-22=0

Wy multiply elements

9a^2+12a-22=0

a = 9; b = 12; c = -22;
Δ = b2-4ac
Δ = 122-4·9·(-22)
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{26}}{2*9}=\frac{-12-6\sqrt{26}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{26}}{2*9}=\frac{-12+6\sqrt{26}}{18}
$