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40=(x-7)(x-1)
We move all terms to the left:
40-((x-7)(x-1))=0
We multiply parentheses ..
-((+x^2-1x-7x+7))+40=0
We calculate terms in parentheses: -((+x^2-1x-7x+7)), so:We get rid of parentheses
(+x^2-1x-7x+7)
We get rid of parentheses
x^2-1x-7x+7
We add all the numbers together, and all the variables
x^2-8x+7
Back to the equation:
-(x^2-8x+7)
-x^2+8x-7+40=0
We add all the numbers together, and all the variables
-1x^2+8x+33=0
a = -1; b = 8; c = +33;
Δ = b2-4ac
Δ = 82-4·(-1)·33
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-14}{2*-1}=\frac{-22}{-2} =+11 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+14}{2*-1}=\frac{6}{-2} =-3 $
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