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x^2-14x=-14
We move all terms to the left:
x^2-14x-(-14)=0
We add all the numbers together, and all the variables
x^2-14x+14=0
a = 1; b = -14; c = +14;
Δ = b2-4ac
Δ = -142-4·1·14
Δ = 140
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{35}}{2*1}=\frac{14-2\sqrt{35}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{35}}{2*1}=\frac{14+2\sqrt{35}}{2} $
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