-5x(-2x-5)-x-1=-12

Solution for -5x(-2x-5)-x-1=-12 equation:

-5x(-2x-5)-x-1=-12

We move all terms to the left:

-5x(-2x-5)-x-1-(-12)=0

We add all the numbers together, and all the variables

-1x-5x(-2x-5)+11=0

We multiply parentheses

10x^2-1x+25x+11=0

We add all the numbers together, and all the variables

10x^2+24x+11=0

a = 10; b = 24; c = +11;
Δ = b2-4ac
Δ = 242-4·10·11
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{34}}{2*10}=\frac{-24-2\sqrt{34}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{34}}{2*10}=\frac{-24+2\sqrt{34}}{20}
$