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(x-4)(x+1)-(7+7)(x-3)=-7x+17
We move all terms to the left:
(x-4)(x+1)-(7+7)(x-3)-(-7x+17)=0
We add all the numbers together, and all the variables
(x-4)(x+1)-14(x-3)-(-7x+17)=0
We multiply parentheses
(x-4)(x+1)-14x-(-7x+17)+42=0
We get rid of parentheses
(x-4)(x+1)-14x+7x-17+42=0
We multiply parentheses ..
(+x^2+x-4x-4)-14x+7x-17+42=0
We add all the numbers together, and all the variables
(+x^2+x-4x-4)-7x+25=0
We get rid of parentheses
x^2+x-4x-7x-4+25=0
We add all the numbers together, and all the variables
x^2-10x+21=0
a = 1; b = -10; c = +21;
Δ = b2-4ac
Δ = -102-4·1·21
Δ = 16
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{16}=4$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4}{2*1}=\frac{6}{2} =3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4}{2*1}=\frac{14}{2} =7 $
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