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756=450+0.5x(x+1)
We move all terms to the left:
756-(450+0.5x(x+1))=0
We calculate terms in parentheses: -(450+0.5x(x+1)), so:We get rid of parentheses
450+0.5x(x+1)
determiningTheFunctionDomain 0.5x(x+1)+450
We multiply parentheses
0x^2+0x+450
We add all the numbers together, and all the variables
x^2+x+450
Back to the equation:
-(x^2+x+450)
-x^2-x-450+756=0
We add all the numbers together, and all the variables
-1x^2-1x+306=0
a = -1; b = -1; c = +306;
Δ = b2-4ac
Δ = -12-4·(-1)·306
Δ = 1225
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{1225}=35$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-35}{2*-1}=\frac{-34}{-2} =+17 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+35}{2*-1}=\frac{36}{-2} =-18 $
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