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X2-5X=48
We move all terms to the left:
X2-5X-(48)=0
We add all the numbers together, and all the variables
X^2-5X-48=0
a = 1; b = -5; c = -48;
Δ = b2-4ac
Δ = -52-4·1·(-48)
Δ = 217
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{-(-5)-\sqrt{217}}{2*1}=\frac{5-\sqrt{217}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{217}}{2*1}=\frac{5+\sqrt{217}}{2} $
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