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-x2+14x=-122
We move all terms to the left:
-x2+14x-(-122)=0
We add all the numbers together, and all the variables
-1x^2+14x+122=0
a = -1; b = 14; c = +122;
Δ = b2-4ac
Δ = 142-4·(-1)·122
Δ = 684
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{19}}{2*-1}=\frac{-14-6\sqrt{19}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{19}}{2*-1}=\frac{-14+6\sqrt{19}}{-2} $
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