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7+6x-x2=x+1
We move all terms to the left:
7+6x-x2-(x+1)=0
We add all the numbers together, and all the variables
-1x^2+6x-(x+1)+7=0
We get rid of parentheses
-1x^2+6x-x-1+7=0
We add all the numbers together, and all the variables
-1x^2+5x+6=0
a = -1; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-1)·6
Δ = 49
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{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*-1}=\frac{-12}{-2} =+6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*-1}=\frac{2}{-2} =-1 $
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