a^2-7a=-11

Solution for a^2-7a=-11 equation:

a^2-7a=-11

We move all terms to the left:

a^2-7a-(-11)=0

We add all the numbers together, and all the variables

a^2-7a+11=0

a = 1; b = -7; c = +11;
Δ = b2-4ac
Δ = -72-4·1·11
Δ = 5
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{-(-7)-\sqrt{5}}{2*1}=\frac{7-\sqrt{5}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{5}}{2*1}=\frac{7+\sqrt{5}}{2}
$