85=-(d-12)(d+8)

Solution for 85=-(d-12)(d+8) equation:

85=-(d-12)(d+8)

We move all terms to the left:

85-(-(d-12)(d+8))=0

We multiply parentheses ..

-(-(+d^2+8d-12d-96))+85=0


We calculate terms in parentheses: -(-(+d^2+8d-12d-96)), so:

-(+d^2+8d-12d-96)

We get rid of parentheses

-d^2-8d+12d+96

We add all the numbers together, and all the variables

-1d^2+4d+96

Back to the equation:

-(-1d^2+4d+96)


We get rid of parentheses

1d^2-4d-96+85=0

We add all the numbers together, and all the variables

d^2-4d-11=0

a = 1; b = -4; c = -11;
Δ = b2-4ac
Δ = -42-4·1·(-11)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{15}}{2*1}=\frac{4-2\sqrt{15}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{15}}{2*1}=\frac{4+2\sqrt{15}}{2}
$