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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-(-7x^2-49x-1x-7)-36=0

We get rid of parentheses

7x^2+49x+1x+7-36=0

We add all the numbers together, and all the variables

7x^2+50x-29=0

a = 7; b = 50; c = -29;
Δ = b2-4ac
Δ = 502-4·7·(-29)
Δ = 3312
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:

$\sqrt{\Delta}=\sqrt{3312}=\sqrt{144*23}=\sqrt{144}*\sqrt{23}=12\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-12\sqrt{23}}{2*7}=\frac{-50-12\sqrt{23}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+12\sqrt{23}}{2*7}=\frac{-50+12\sqrt{23}}{14}
$