(1/4)a+(1/3)a+8=22

Solution for (1/4)a+(1/3)a+8=22 equation:

(1/4)a+(1/3)a+8=22

We move all terms to the left:

(1/4)a+(1/3)a+8-(22)=0


Domain of the equation: 4)a!=0

a!=0/1

a!=0

a∈R



Domain of the equation: 3)a!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

(+1/4)a+(+1/3)a+8-22=0

We add all the numbers together, and all the variables

(+1/4)a+(+1/3)a-14=0

We multiply parentheses

a^2+a^2-14=0

We add all the numbers together, and all the variables

2a^2-14=0

a = 2; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·2·(-14)
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*2}=\frac{0-4\sqrt{7}}{4}
=-\frac{4\sqrt{7}}{4}
=-\sqrt{7}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*2}=\frac{0+4\sqrt{7}}{4}
=\frac{4\sqrt{7}}{4}
=\sqrt{7}
$