2/3a+1/4a-8=7

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Solution for 2/3a+1/4a-8=7 equation: 



2/3a+1/4a-8=7

We move all terms to the left:

2/3a+1/4a-8-(7)=0



Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R





Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



We add all the numbers together, and all the variables

2/3a+1/4a-15=0

We calculate fractions


8a/12a^2+3a/12a^2-15=0

We multiply all the terms by the denominator


8a+3a-15*12a^2=0

We add all the numbers together, and all the variables

11a-15*12a^2=0

Wy multiply elements

-180a^2+11a=0

a = -180; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-180)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$


$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-180}=\frac{-22}{-360}
=11/180
$


$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-180}=\frac{0}{-360}
=0
$

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