a+6=-3/2a+1

Solution for a+6=-3/2a+1 equation:

a+6=-3/2a+1

We move all terms to the left:

a+6-(-3/2a+1)=0


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

a∈R


We get rid of parentheses

a+3/2a-1+6=0

We multiply all the terms by the denominator


a*2a-1*2a+6*2a+3=0

Wy multiply elements

2a^2-2a+12a+3=0

We add all the numbers together, and all the variables

2a^2+10a+3=0

a = 2; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·2·3
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{19}}{2*2}=\frac{-10-2\sqrt{19}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{19}}{2*2}=\frac{-10+2\sqrt{19}}{4}
$