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1+x(x+1)=156
We move all terms to the left:
1+x(x+1)-(156)=0
We add all the numbers together, and all the variables
x(x+1)-155=0
We multiply parentheses
x^2+x-155=0
a = 1; b = 1; c = -155;
Δ = b2-4ac
Δ = 12-4·1·(-155)
Δ = 621
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{69}}{2*1}=\frac{-1-3\sqrt{69}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{69}}{2*1}=\frac{-1+3\sqrt{69}}{2} $
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