5x(-3x)-6x=-1

Solution for 5x(-3x)-6x=-1 equation:

5x(-3x)-6x=-1

We move all terms to the left:

5x(-3x)-6x-(-1)=0

We add all the numbers together, and all the variables

-6x+5x(-3x)+1=0

We multiply parentheses

-15x^2-6x+1=0

a = -15; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-15)·1
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{6}}{2*-15}=\frac{6-4\sqrt{6}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{6}}{2*-15}=\frac{6+4\sqrt{6}}{-30}
$