3a^2-2(a+5)a=-1

Solution for 3a^2-2(a+5)a=-1 equation:

3a^2-2(a+5)a=-1

We move all terms to the left:

3a^2-2(a+5)a-(-1)=0

We add all the numbers together, and all the variables

3a^2-2(a+5)a+1=0

We multiply parentheses

3a^2-2a^2-10a+1=0

We add all the numbers together, and all the variables

a^2-10a+1=0

a = 1; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·1·1
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{6}}{2*1}=\frac{10-4\sqrt{6}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{6}}{2*1}=\frac{10+4\sqrt{6}}{2}
$