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x^2-19x=-14
We move all terms to the left:
x^2-19x-(-14)=0
We add all the numbers together, and all the variables
x^2-19x+14=0
a = 1; b = -19; c = +14;
Δ = b2-4ac
Δ = -192-4·1·14
Δ = 305
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{305}}{2*1}=\frac{19-\sqrt{305}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{305}}{2*1}=\frac{19+\sqrt{305}}{2} $
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