1/4a+1/3a+8=23

Solution for 1/4a+1/3a+8=23 equation:

1/4a+1/3a+8=23

We move all terms to the left:

1/4a+1/3a+8-(23)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

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

We calculate fractions


3a/12a^2+4a/12a^2-15=0

We multiply all the terms by the denominator


3a+4a-15*12a^2=0

We add all the numbers together, and all the variables

7a-15*12a^2=0

Wy multiply elements

-180a^2+7a=0

a = -180; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-180)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-180}=\frac{-14}{-360}
=7/180
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-180}=\frac{0}{-360}
=0
$