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0=x^2+6x-24
We move all terms to the left:
0-(x^2+6x-24)=0
We add all the numbers together, and all the variables
-(x^2+6x-24)=0
We get rid of parentheses
-x^2-6x+24=0
We add all the numbers together, and all the variables
-1x^2-6x+24=0
a = -1; b = -6; c = +24;
Δ = b2-4ac
Δ = -62-4·(-1)·24
Δ = 132
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{33}}{2*-1}=\frac{6-2\sqrt{33}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{33}}{2*-1}=\frac{6+2\sqrt{33}}{-2} $
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