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(X-7)(X+3)-(X+2)+5=0
We get rid of parentheses
(X-7)(X+3)-X-2+5=0
We multiply parentheses ..
(+X^2+3X-7X-21)-X-2+5=0
We add all the numbers together, and all the variables
(+X^2+3X-7X-21)-1X+3=0
We get rid of parentheses
X^2+3X-7X-1X-21+3=0
We add all the numbers together, and all the variables
X^2-5X-18=0
a = 1; b = -5; c = -18;
Δ = b2-4ac
Δ = -52-4·1·(-18)
Δ = 97
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{97}}{2*1}=\frac{5-\sqrt{97}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{97}}{2*1}=\frac{5+\sqrt{97}}{2} $
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