-36=(17-x)x-2

Solution for -36=(17-x)x-2 equation:

-36=(17-x)x-2

We move all terms to the left:

-36-((17-x)x-2)=0

We add all the numbers together, and all the variables

-((-1x+17)x-2)-36=0


We calculate terms in parentheses: -((-1x+17)x-2), so:

(-1x+17)x-2

We multiply parentheses

-1x^2+17x-2

Back to the equation:

-(-1x^2+17x-2)


We get rid of parentheses

1x^2-17x+2-36=0

We add all the numbers together, and all the variables

x^2-17x-34=0

a = 1; b = -17; c = -34;
Δ = b2-4ac
Δ = -172-4·1·(-34)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-5\sqrt{17}}{2*1}=\frac{17-5\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+5\sqrt{17}}{2*1}=\frac{17+5\sqrt{17}}{2}
$