X*x+(x+1)(x+1)=85

Solution for X*x+(x+1)(x+1)=85 equation:

X*X+(X+1)(X+1)=85

We move all terms to the left:

X*X+(X+1)(X+1)-(85)=0

Wy multiply elements

X^2+(X+1)(X+1)-85=0

We multiply parentheses ..

X^2+(+X^2+X+X+1)-85=0

We get rid of parentheses

X^2+X^2+X+X+1-85=0

We add all the numbers together, and all the variables

2X^2+2X-84=0

a = 2; b = 2; c = -84;
Δ = b2-4ac
Δ = 22-4·2·(-84)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-26}{2*2}=\frac{-28}{4}
=-7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+26}{2*2}=\frac{24}{4}
=6
$