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(35-x)*x=276
We move all terms to the left:
(35-x)*x-(276)=0
We add all the numbers together, and all the variables
(-1x+35)*x-276=0
We multiply parentheses
-1x^2+35x-276=0
a = -1; b = 35; c = -276;
Δ = b2-4ac
Δ = 352-4·(-1)·(-276)
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-11}{2*-1}=\frac{-46}{-2} =+23 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+11}{2*-1}=\frac{-24}{-2} =+12 $
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