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(x-2)(x+9)=17
We move all terms to the left:
(x-2)(x+9)-(17)=0
We multiply parentheses ..
(+x^2+9x-2x-18)-17=0
We get rid of parentheses
x^2+9x-2x-18-17=0
We add all the numbers together, and all the variables
x^2+7x-35=0
a = 1; b = 7; c = -35;
Δ = b2-4ac
Δ = 72-4·1·(-35)
Δ = 189
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{21}}{2*1}=\frac{-7-3\sqrt{21}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{21}}{2*1}=\frac{-7+3\sqrt{21}}{2} $
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