3/4a+14=8+2a

Solution for 3/4a+14=8+2a equation:

3/4a+14=8+2a

We move all terms to the left:

3/4a+14-(8+2a)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We add all the numbers together, and all the variables

3/4a-(2a+8)+14=0

We get rid of parentheses

3/4a-2a-8+14=0

We multiply all the terms by the denominator


-2a*4a-8*4a+14*4a+3=0

Wy multiply elements

-8a^2-32a+56a+3=0

We add all the numbers together, and all the variables

-8a^2+24a+3=0

a = -8; b = 24; c = +3;
Δ = b2-4ac
Δ = 242-4·(-8)·3
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{42}}{2*-8}=\frac{-24-4\sqrt{42}}{-16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{42}}{2*-8}=\frac{-24+4\sqrt{42}}{-16}
$