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x(x+1)=377610
We move all terms to the left:
x(x+1)-(377610)=0
We multiply parentheses
x^2+x-377610=0
a = 1; b = 1; c = -377610;
Δ = b2-4ac
Δ = 12-4·1·(-377610)
Δ = 1510441
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1510441}=1229$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1229}{2*1}=\frac{-1230}{2} =-615 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1229}{2*1}=\frac{1228}{2} =614 $
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