2+7a=29+a2-4a

Solution for 2+7a=29+a2-4a equation:

2+7a=29+a2-4a

We move all terms to the left:

2+7a-(29+a2-4a)=0

We add all the numbers together, and all the variables

-(+a^2-4a+29)+7a+2=0

We get rid of parentheses

-a^2+4a+7a-29+2=0

We add all the numbers together, and all the variables

-1a^2+11a-27=0

a = -1; b = 11; c = -27;
Δ = b2-4ac
Δ = 112-4·(-1)·(-27)
Δ = 13
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{-(11)-\sqrt{13}}{2*-1}=\frac{-11-\sqrt{13}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{13}}{2*-1}=\frac{-11+\sqrt{13}}{-2}
$