2/3a-1-1/4a=-6

Solution for 2/3a-1-1/4a=-6 equation:

2/3a-1-1/4a=-6

We move all terms to the left:

2/3a-1-1/4a-(-6)=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+5=0

We calculate fractions


8a/12a^2+(-3a)/12a^2+5=0

We multiply all the terms by the denominator


8a+(-3a)+5*12a^2=0

Wy multiply elements

60a^2+8a+(-3a)=0

We get rid of parentheses

60a^2+8a-3a=0

We add all the numbers together, and all the variables

60a^2+5a=0

a = 60; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·60·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*60}=\frac{-10}{120}
=-1/12
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*60}=\frac{0}{120}
=0
$