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(x-2)(x-3)=84
We move all terms to the left:
(x-2)(x-3)-(84)=0
We multiply parentheses ..
(+x^2-3x-2x+6)-84=0
We get rid of parentheses
x^2-3x-2x+6-84=0
We add all the numbers together, and all the variables
x^2-5x-78=0
a = 1; b = -5; c = -78;
Δ = b2-4ac
Δ = -52-4·1·(-78)
Δ = 337
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{337}}{2*1}=\frac{5-\sqrt{337}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{337}}{2*1}=\frac{5+\sqrt{337}}{2} $
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