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x=x^2+7x-66
We move all terms to the left:
x-(x^2+7x-66)=0
We get rid of parentheses
-x^2+x-7x+66=0
We add all the numbers together, and all the variables
-1x^2-6x+66=0
a = -1; b = -6; c = +66;
Δ = b2-4ac
Δ = -62-4·(-1)·66
Δ = 300
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10\sqrt{3}}{2*-1}=\frac{6-10\sqrt{3}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10\sqrt{3}}{2*-1}=\frac{6+10\sqrt{3}}{-2} $
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