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(41-x)*x/2=210
We move all terms to the left:
(41-x)*x/2-(210)=0
We add all the numbers together, and all the variables
(-1x+41)*x/2-210=0
We multiply all the terms by the denominator
(-1x+41)*x-210*2=0
We add all the numbers together, and all the variables
(-1x+41)*x-420=0
We multiply parentheses
-1x^2+41x-420=0
a = -1; b = 41; c = -420;
Δ = b2-4ac
Δ = 412-4·(-1)·(-420)
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-1}{2*-1}=\frac{-42}{-2} =+21 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+1}{2*-1}=\frac{-40}{-2} =+20 $
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