6/a-2=3/4a-9

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Solution for 6/a-2=3/4a-9 equation: 



6/a-2=3/4a-9

We move all terms to the left:

6/a-2-(3/4a-9)=0



Domain of the equation: a!=0

a∈R





Domain of the equation: 4a-9)!=0

a∈R



We get rid of parentheses

6/a-3/4a+9-2=0

We calculate fractions


24a/4a^2+(-3a)/4a^2+9-2=0

We add all the numbers together, and all the variables

24a/4a^2+(-3a)/4a^2+7=0

We multiply all the terms by the denominator


24a+(-3a)+7*4a^2=0

Wy multiply elements

28a^2+24a+(-3a)=0

We get rid of parentheses

28a^2+24a-3a=0

We add all the numbers together, and all the variables

28a^2+21a=0

a = 28; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·28·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$


$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*28}=\frac{-42}{56}
=-3/4
$


$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*28}=\frac{0}{56}
=0
$

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