0=x^2+12x-110

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Solution for 0=x^2+12x-110 equation:



0=x^2+12x-110
We move all terms to the left:
0-(x^2+12x-110)=0
We add all the numbers together, and all the variables
-(x^2+12x-110)=0
We get rid of parentheses
-x^2-12x+110=0
We add all the numbers together, and all the variables
-1x^2-12x+110=0
a = -1; b = -12; c = +110;
Δ = b2-4ac
Δ = -122-4·(-1)·110
Δ = 584
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:
$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{146}}{2*-1}=\frac{12-2\sqrt{146}}{-2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{146}}{2*-1}=\frac{12+2\sqrt{146}}{-2} $

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