6x(x+3)-5=64

Solution for 6x(x+3)-5=64 equation:

6x(x+3)-5=64

We move all terms to the left:

6x(x+3)-5-(64)=0

We add all the numbers together, and all the variables

6x(x+3)-69=0

We multiply parentheses

6x^2+18x-69=0

a = 6; b = 18; c = -69;
Δ = b2-4ac
Δ = 182-4·6·(-69)
Δ = 1980
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1980}=\sqrt{36*55}=\sqrt{36}*\sqrt{55}=6\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{55}}{2*6}=\frac{-18-6\sqrt{55}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{55}}{2*6}=\frac{-18+6\sqrt{55}}{12}
$