(12a*4a)/2=432

Solution for (12a*4a)/2=432 equation:

(12a*4a)/2=432

We move all terms to the left:

(12a*4a)/2-(432)=0

We add all the numbers together, and all the variables

(+12a*4a)/2-432=0

We multiply all the terms by the denominator


(+12a*4a)-432*2=0

We add all the numbers together, and all the variables

(+12a*4a)-864=0

We get rid of parentheses

12a*4a-864=0

Wy multiply elements

48a^2-864=0

a = 48; b = 0; c = -864;
Δ = b2-4ac
Δ = 02-4·48·(-864)
Δ = 165888
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:

$\sqrt{\Delta}=\sqrt{165888}=\sqrt{82944*2}=\sqrt{82944}*\sqrt{2}=288\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-288\sqrt{2}}{2*48}=\frac{0-288\sqrt{2}}{96}
=-\frac{288\sqrt{2}}{96}
=-3\sqrt{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+288\sqrt{2}}{2*48}=\frac{0+288\sqrt{2}}{96}
=\frac{288\sqrt{2}}{96}
=3\sqrt{2}
$