a^2+9a=7a+27

Solution for a^2+9a=7a+27 equation:

a^2+9a=7a+27

We move all terms to the left:

a^2+9a-(7a+27)=0

We get rid of parentheses

a^2+9a-7a-27=0

We add all the numbers together, and all the variables

a^2+2a-27=0

a = 1; b = 2; c = -27;
Δ = b2-4ac
Δ = 22-4·1·(-27)
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{-(2)-4\sqrt{7}}{2*1}=\frac{-2-4\sqrt{7}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{7}}{2*1}=\frac{-2+4\sqrt{7}}{2}
$