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+2)x-1)+84=0


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

(2x+2)x-1

We multiply parentheses

2x^2+2x-1

Back to the equation:

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


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = -2; c = +85;
Δ = b2-4ac
Δ = -22-4·(-2)·85
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{19}}{2*-2}=\frac{2-6\sqrt{19}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{19}}{2*-2}=\frac{2+6\sqrt{19}}{-4}
$