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m2+5-m=65
We move all terms to the left:
m2+5-m-(65)=0
We add all the numbers together, and all the variables
m^2-1m-60=0
a = 1; b = -1; c = -60;
Δ = b2-4ac
Δ = -12-4·1·(-60)
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{241}}{2*1}=\frac{1-\sqrt{241}}{2} $$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{241}}{2*1}=\frac{1+\sqrt{241}}{2} $
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