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2x-3x=x^2+6x+7
We move all terms to the left:
2x-3x-(x^2+6x+7)=0
We add all the numbers together, and all the variables
-1x-(x^2+6x+7)=0
We get rid of parentheses
-x^2-1x-6x-7=0
We add all the numbers together, and all the variables
-1x^2-7x-7=0
a = -1; b = -7; c = -7;
Δ = b2-4ac
Δ = -72-4·(-1)·(-7)
Δ = 21
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{-(-7)-\sqrt{21}}{2*-1}=\frac{7-\sqrt{21}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{21}}{2*-1}=\frac{7+\sqrt{21}}{-2} $
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