72+27a+a2=918+3a

Solution for 72+27a+a2=918+3a equation:

72+27a+a2=918+3a

We move all terms to the left:

72+27a+a2-(918+3a)=0

We add all the numbers together, and all the variables

27a+a2-(3a+918)+72=0

We add all the numbers together, and all the variables

a^2+27a-(3a+918)+72=0

We get rid of parentheses

a^2+27a-3a-918+72=0

We add all the numbers together, and all the variables

a^2+24a-846=0

a = 1; b = 24; c = -846;
Δ = b2-4ac
Δ = 242-4·1·(-846)
Δ = 3960
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:

$\sqrt{\Delta}=\sqrt{3960}=\sqrt{36*110}=\sqrt{36}*\sqrt{110}=6\sqrt{110}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{110}}{2*1}=\frac{-24-6\sqrt{110}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{110}}{2*1}=\frac{-24+6\sqrt{110}}{2}
$