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(x)(x+2)=161.5
We move all terms to the left:
(x)(x+2)-(161.5)=0
We add all the numbers together, and all the variables
x(x+2)-161.5=0
We multiply parentheses
x^2+2x-161.5=0
a = 1; b = 2; c = -161.5;
Δ = b2-4ac
Δ = 22-4·1·(-161.5)
Δ = 650
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{650}=\sqrt{25*26}=\sqrt{25}*\sqrt{26}=5\sqrt{26}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-5\sqrt{26}}{2*1}=\frac{-2-5\sqrt{26}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+5\sqrt{26}}{2*1}=\frac{-2+5\sqrt{26}}{2} $
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