2a-7=1/3a+0,5

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Solution for 2a-7=1/3a+0,5 equation:



2a-7=1/3a+0.5
We move all terms to the left:
2a-7-(1/3a+0.5)=0
Domain of the equation: 3a+0.5)!=0
a∈R
We get rid of parentheses
2a-1/3a-0.5-7=0
We multiply all the terms by the denominator
2a*3a-(0.5)*3a-7*3a-1=0
We multiply parentheses
2a*3a-1.5a-7*3a-1=0
Wy multiply elements
6a^2-1.5a-21a-1=0
We add all the numbers together, and all the variables
6a^2-22.5a-1=0
a = 6; b = -22.5; c = -1;
Δ = b2-4ac
Δ = -22.52-4·6·(-1)
Δ = 530.25
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{-(-22.5)-\sqrt{530.25}}{2*6}=\frac{22.5-\sqrt{530.25}}{12} $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22.5)+\sqrt{530.25}}{2*6}=\frac{22.5+\sqrt{530.25}}{12} $

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