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(d-2)(d-6)=83
We move all terms to the left:
(d-2)(d-6)-(83)=0
We multiply parentheses ..
(+d^2-6d-2d+12)-83=0
We get rid of parentheses
d^2-6d-2d+12-83=0
We add all the numbers together, and all the variables
d^2-8d-71=0
a = 1; b = -8; c = -71;
Δ = b2-4ac
Δ = -82-4·1·(-71)
Δ = 348
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}$$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{87}}{2*1}=\frac{8-2\sqrt{87}}{2} $$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{87}}{2*1}=\frac{8+2\sqrt{87}}{2} $
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