84=(x-3+x-1)x-1

Solution for 84=(x-3+x-1)x-1 equation:

84=(x-3+x-1)x-1

We move all terms to the left:

84-((x-3+x-1)x-1)=0

We add all the numbers together, and all the variables

-((2x-4)x-1)+84=0


We calculate terms in parentheses: -((2x-4)x-1), so:

(2x-4)x-1

We multiply parentheses

2x^2-4x-1

Back to the equation:

-(2x^2-4x-1)


We get rid of parentheses

-2x^2+4x+1+84=0

We add all the numbers together, and all the variables

-2x^2+4x+85=0

a = -2; b = 4; c = +85;
Δ = b2-4ac
Δ = 42-4·(-2)·85
Δ = 696
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:

$\sqrt{\Delta}=\sqrt{696}=\sqrt{4*174}=\sqrt{4}*\sqrt{174}=2\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{174}}{2*-2}=\frac{-4-2\sqrt{174}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{174}}{2*-2}=\frac{-4+2\sqrt{174}}{-4}
$