a2-11a=-27

Solution for a2-11a=-27 equation:

a2-11a=-27

We move all terms to the left:

a2-11a-(-27)=0

We add all the numbers together, and all the variables

a^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}
$