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(x-1)(x-7)=5
We move all terms to the left:
(x-1)(x-7)-(5)=0
We multiply parentheses ..
(+x^2-7x-1x+7)-5=0
We get rid of parentheses
x^2-7x-1x+7-5=0
We add all the numbers together, and all the variables
x^2-8x+2=0
a = 1; b = -8; c = +2;
Δ = b2-4ac
Δ = -82-4·1·2
Δ = 56
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{14}}{2*1}=\frac{8-2\sqrt{14}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{14}}{2*1}=\frac{8+2\sqrt{14}}{2} $
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