-5a(6+6a)=-61

Solution for -5a(6+6a)=-61 equation:

-5a(6+6a)=-61

We move all terms to the left:

-5a(6+6a)-(-61)=0

We add all the numbers together, and all the variables

-5a(6a+6)-(-61)=0

We add all the numbers together, and all the variables

-5a(6a+6)+61=0

We multiply parentheses

-30a^2-30a+61=0

a = -30; b = -30; c = +61;
Δ = b2-4ac
Δ = -302-4·(-30)·61
Δ = 8220
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:

$\sqrt{\Delta}=\sqrt{8220}=\sqrt{4*2055}=\sqrt{4}*\sqrt{2055}=2\sqrt{2055}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{2055}}{2*-30}=\frac{30-2\sqrt{2055}}{-60}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{2055}}{2*-30}=\frac{30+2\sqrt{2055}}{-60}
$