-5-x(x-7)+6x=-1

Solution for -5-x(x-7)+6x=-1 equation:

-5-x(x-7)+6x=-1

We move all terms to the left:

-5-x(x-7)+6x-(-1)=0

We add all the numbers together, and all the variables

6x-x(x-7)-4=0

We multiply parentheses

-x^2+6x+7x-4=0

We add all the numbers together, and all the variables

-1x^2+13x-4=0

a = -1; b = 13; c = -4;
Δ = b2-4ac
Δ = 132-4·(-1)·(-4)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3\sqrt{17}}{2*-1}=\frac{-13-3\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3\sqrt{17}}{2*-1}=\frac{-13+3\sqrt{17}}{-2}
$