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180=x^2+6x-24
We move all terms to the left:
180-(x^2+6x-24)=0
We get rid of parentheses
-x^2-6x+24+180=0
We add all the numbers together, and all the variables
-1x^2-6x+204=0
a = -1; b = -6; c = +204;
Δ = b2-4ac
Δ = -62-4·(-1)·204
Δ = 852
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{213}}{2*-1}=\frac{6-2\sqrt{213}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{213}}{2*-1}=\frac{6+2\sqrt{213}}{-2} $
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