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12.7=8.7728551+241.0072318x+-13.20673942x^2
We move all terms to the left:
12.7-(8.7728551+241.0072318x+-13.20673942x^2)=0
We use the square of the difference formula
-(8.7728551+241.0072318x-13.20673942x^2)+12.7=0
We get rid of parentheses
13.20673942x^2-241.0072318x-8.7728551+12.7=0
We add all the numbers together, and all the variables
13.20673942x^2-241.0072318x+3.9271449=0
a = 13.20673942; b = -241.0072318; c = +3.9271449;
Δ = b2-4ac
Δ = -241.00723182-4·13.20673942·3.9271449
Δ = 57877.026662463
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-241.0072318)-\sqrt{57877.026662463}}{2*13.20673942}=\frac{241.0072318-\sqrt{57877.026662463}}{26.41347884} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-241.0072318)+\sqrt{57877.026662463}}{2*13.20673942}=\frac{241.0072318+\sqrt{57877.026662463}}{26.41347884} $
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