4/5a-2+0.5a=11

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Solution for 4/5a-2+0.5a=11 equation: 



4/5a-2+0.5a=11

We move all terms to the left:

4/5a-2+0.5a-(11)=0



Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



We add all the numbers together, and all the variables

0.5a+4/5a-13=0

We multiply all the terms by the denominator


(0.5a)*5a-13*5a+4=0

We add all the numbers together, and all the variables

(+0.5a)*5a-13*5a+4=0

We multiply parentheses

0a^2-13*5a+4=0

Wy multiply elements

0a^2-65a+4=0

We add all the numbers together, and all the variables

a^2-65a+4=0

a = 1; b = -65; c = +4;
Δ = b2-4ac
Δ = -652-4·1·4
Δ = 4209
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{-(-65)-\sqrt{4209}}{2*1}=\frac{65-\sqrt{4209}}{2}
$


$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{4209}}{2*1}=\frac{65+\sqrt{4209}}{2}
$

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