4+a-12+a(3/4)=8

Solution for 4+a-12+a(3/4)=8 equation:

4+a-12+a(3/4)=8

We move all terms to the left:

4+a-12+a(3/4)-(8)=0

We add all the numbers together, and all the variables

a+a(+3/4)+4-12-8=0

We add all the numbers together, and all the variables

a+a(+3/4)-16=0

We multiply parentheses

3a^2+a-16=0

a = 3; b = 1; c = -16;
Δ = b2-4ac
Δ = 12-4·3·(-16)
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{193}}{2*3}=\frac{-1-\sqrt{193}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{193}}{2*3}=\frac{-1+\sqrt{193}}{6}
$