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X2-4X=77
We move all terms to the left:
X2-4X-(77)=0
We add all the numbers together, and all the variables
X^2-4X-77=0
a = 1; b = -4; c = -77;
Δ = b2-4ac
Δ = -42-4·1·(-77)
Δ = 324
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{324}=18$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-18}{2*1}=\frac{-14}{2} =-7 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+18}{2*1}=\frac{22}{2} =11 $
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