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X(5+X)+2X=-1
We move all terms to the left:
X(5+X)+2X-(-1)=0
We add all the numbers together, and all the variables
X(X+5)+2X-(-1)=0
We add all the numbers together, and all the variables
2X+X(X+5)+1=0
We multiply parentheses
X^2+2X+5X+1=0
We add all the numbers together, and all the variables
X^2+7X+1=0
a = 1; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·1·1
Δ = 45
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{5}}{2*1}=\frac{-7-3\sqrt{5}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{5}}{2*1}=\frac{-7+3\sqrt{5}}{2} $
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