22-(3/2a+1)=2a

Solution for 22-(3/2a+1)=2a equation:

22-(3/2a+1)=2a

We move all terms to the left:

22-(3/2a+1)-(2a)=0


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

a∈R


We add all the numbers together, and all the variables

-2a-(3/2a+1)+22=0

We get rid of parentheses

-2a-3/2a-1+22=0

We multiply all the terms by the denominator


-2a*2a-1*2a+22*2a-3=0

Wy multiply elements

-4a^2-2a+44a-3=0

We add all the numbers together, and all the variables

-4a^2+42a-3=0

a = -4; b = 42; c = -3;
Δ = b2-4ac
Δ = 422-4·(-4)·(-3)
Δ = 1716
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:

$\sqrt{\Delta}=\sqrt{1716}=\sqrt{4*429}=\sqrt{4}*\sqrt{429}=2\sqrt{429}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{429}}{2*-4}=\frac{-42-2\sqrt{429}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{429}}{2*-4}=\frac{-42+2\sqrt{429}}{-8}
$