-1x(1+7x)-6(-7-1x)=36

Solution for -1x(1+7x)-6(-7-1x)=36 equation:

-1x(1+7x)-6(-7-1x)=36

We move all terms to the left:

-1x(1+7x)-6(-7-1x)-(36)=0

We add all the numbers together, and all the variables

-1x(7x+1)-6(-1x-7)-36=0

We multiply parentheses

-7x^2-x+6x+42-36=0

We add all the numbers together, and all the variables

-7x^2+5x+6=0

a = -7; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-7)·6
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{193}}{2*-7}=\frac{-5-\sqrt{193}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{193}}{2*-7}=\frac{-5+\sqrt{193}}{-14}
$