1/2a+0.2=-1+3a

Solution for 1/2a+0.2=-1+3a equation:

1/2a+0.2=-1+3a

We move all terms to the left:

1/2a+0.2-(-1+3a)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

1/2a-(3a-1)+0.2=0

We get rid of parentheses

1/2a-3a+1+0.2=0

We multiply all the terms by the denominator


-3a*2a+1*2a+(0.2)*2a+1=0

We multiply parentheses

-3a*2a+1*2a+0.4a+1=0

Wy multiply elements

-6a^2+2a+0.4a+1=0

We add all the numbers together, and all the variables

-6a^2+2.4a+1=0

a = -6; b = 2.4; c = +1;
Δ = b2-4ac
Δ = 2.42-4·(-6)·1
Δ = 29.76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2.4)-\sqrt{29.76}}{2*-6}=\frac{-2.4-\sqrt{29.76}}{-12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.4)+\sqrt{29.76}}{2*-6}=\frac{-2.4+\sqrt{29.76}}{-12}
$